Illustrative Math Alignment: Grade 6 Unit 7

Rational Numbers

Lesson 17: Common Multiples

Use the following Media4Math resources with this Illustrative Math lesson.

Title	Body	Curriculum Nodes
Closed Captioned Video: Percents: Multiple Percents	Closed Captioned Video: Percents: Multiple Percents Topic Percents Description This video demonstrates how to handle multiple percentage changes applied sequentially, including discounts and price fluctuations. Examples include double-discounted items, stock price variations, and gasoline price changes. Applications emphasize consolidating multiple percents into single calculations for efficiency in financial and retail scenarios.	Percents
Closed Captioned Video: Percents: Percents and Multiples of Numbers	Closed Captioned Video: Percents: Percents and Multiples of Numbers Topic Percents Description The video explains the distinction between percent growth and multiple growth. Examples include doubling heights, stock price increases, and oil price changes. Applications emphasize clear understanding of percent versus multiplier concepts in finance and everyday math.	Percents
Definition--Factors and Multiples--Area Models for Factors	Area Models for Factors Topic Factors and Multiples Definition Factors are numbers that divide another number without leaving a remainder, while multiples are the result of multiplying a number by an integer. Description Understanding factors and multiples is crucial in mathematics, particularly in number theory and algebra. Factors are the building blocks of numbers, representing the integers that can be multiplied together to produce another number. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12. Multiples, on the other hand, are the product of a number and any integer. For instance, the multiples of 5 include 5, 10, 15, 20, and so on.	Numerical Expressions
Definition--Factors and Multiples--Common Factors	Common Factors Topic Factors and Multiples Definition A common factor is a number that divides two or more numbers exactly without leaving a remainder. Description Common factors are integral to understanding the mathematical concepts of factors and multiples. They are the numbers that can divide two or more given numbers without leaving a remainder. For example, if you consider the numbers 12 and 18, their common factors are 1, 2, 3, and 6. This is because these numbers can divide both 12 and 18 exactly, with no remainder.	Numerical Expressions
Definition--Factors and Multiples--Common Multiples	Common Multiples Topic Factors and Multiples Definition A common multiple is a number that is a multiple of two or more numbers. Description In the context of factors and multiples, understanding common multiples is crucial for solving various mathematical problems, particularly those involving fractions, least common multiples (LCM), and algebraic expressions. A common multiple of a set of numbers is a number that each of the numbers in the set divides without leaving a remainder. For example, the common multiples of 4 and 6 include 12, 24, 36, and so on. The smallest of these, 12, is known as the least common multiple (LCM).	Numerical Expressions
Definition--Factors and Multiples--Divisor	Divisor Topic Factors and Multiples Definition A divisor is a number that divides another number evenly, leaving no remainder. Description In the context of factors and multiples, a divisor plays a crucial role in understanding the relationships between numbers. A divisor is essentially a factor of a given number, as it divides that number without leaving a remainder. This concept is fundamental to identifying factors and understanding divisibility rules.	Numerical Expressions
Definition--Factors and Multiples--Factor Pairs	Factor Pairs Topic Factors and Multiples Definition Factor pairs are sets of two numbers that, when multiplied together, produce a given number. Description Factor pairs play a crucial role in understanding the relationships between numbers and their factors. They are essential in various mathematical operations, particularly in algebra and number theory. Factor pairs help students visualize the multiplicative structure of numbers and provide a foundation for more advanced concepts such as prime factorization and divisibility rules.	Numerical Expressions
Definition--Factors and Multiples--Factor Tree	Factor Tree Topic Factors and Multiples Definition A factor tree is a graphical method used to break down a number into its prime factors. Description A factor tree is a visual representation that helps in identifying the prime factors of a given number. It starts with the original number at the top and branches downwards, breaking the number into its factors until all the branches end in prime numbers. This method is particularly useful in understanding the concept of prime factorization, which is the process of expressing a number as the product of its prime factors.	Numerical Expressions
Definition--Factors and Multiples--Factoring Algebraic Expressions	Factoring Algebraic Expressions Topic Factors and Multiples Definition Factoring algebraic expressions involves breaking down a polynomial into simpler components called factors that, when multiplied together, give the original polynomial. Description Factoring algebraic expressions is a fundamental concept in algebra that plays a crucial role in simplifying expressions, solving equations, and understanding polynomial functions. This process involves expressing a polynomial as a product of its factors, which are simpler polynomials or numbers. For instance, the polynomial x^2 - 5x + 6 can be factored into (x - 2)(x - 3).	Numerical Expressions
Definition--Factors and Multiples--Factors	Factors Topic Factors and Multiples Definition Factors are numbers that divide evenly into another number without leaving a remainder. Description Factors play a crucial role in understanding the fundamental properties of numbers and their relationships. In the context of factors and multiples, factors are the building blocks that, when multiplied together, create a given number. This concept is essential for various mathematical operations and problem-solving techniques.	Numerical Expressions
Definition--Factors and Multiples--Greatest Common Factor (GCF)	Greatest Common Factor (GCF) Topic Factors and Multiples Definition The Greatest Common Factor (GCF) is the largest number that divides two or more numbers without leaving a remainder. Description The concept of the Greatest Common Factor (GCF) is crucial in the study of factors and multiples. The GCF is used to simplify fractions, find common denominators, and solve problems involving ratios. Understanding the GCF helps in breaking down complex problems into simpler parts, making it easier to handle large numbers and perform arithmetic operations efficiently.	Numerical Expressions
Definition--Factors and Multiples--LCM	Least Common Multiple (LCM) Topic Factors and Multiples Definition The least common multiple (LCM) is the smallest number that is a multiple of two or more numbers. Description The concept of the least common multiple (LCM) is essential in the study of factors and multiples. The LCM of two or more numbers is the smallest number that is evenly divisible by all of the given numbers. This concept is particularly useful in various mathematical operations and problem-solving scenarios.	Numerical Expressions
Definition--Factors and Multiples--Multiple	Multiples Topic Factors and Multiples Definition A multiple is a number that can be divided by another number without leaving a remainder. Description Multiples are fundamental in understanding the relationships between numbers in mathematics. They are particularly relevant when learning about factors and multiples, which are key concepts in elementary and middle school math curricula. A multiple of a number is obtained by multiplying that number by an integer. For example, the multiples of 5 include 5, 10, 15, 20, and so on.	Numerical Expressions
Definition--Factors and Multiples--Multiples of 10	Multiples of 10 Topic Factors and Multiples Definition Multiples of 10 are the numbers that result from multiplying 10 by any whole number. Description Multiples of 10 play a significant role in understanding factors and multiples. These numbers are easily recognizable as they always end in zero and form a predictable pattern on the number line. In the context of factors and multiples, multiples of 10 serve as an excellent example to illustrate the concept of multiples in general.	Numerical Expressions
Definition--Factors and Multiples--Multiples of Unit Fractions	Multiples of Unit Fractions Topic Factors and Multiples Definition Multiples are the results obtained when a number is multiplied by an integer. Description In mathematics, understanding the concept of multiples is crucial, especially when dealing with factors and multiples. A multiple of a number is the product obtained when that number is multiplied by an integer. For example, the multiples of 3 include 3, 6, 9, 12, and so on. This concept is fundamental in various mathematical operations and problem-solving scenarios.	Numerical Expressions
Definition--Factors and Multiples--Prime Factorization	Prime Factorization Topic Factors and Multiples Definition Prime factorization is the process of breaking down a composite number into its prime factors. Description Prime factorization is a fundamental concept in the study of factors and multiples. It involves expressing a composite number as a product of prime numbers. For example, the number 60 can be factorized into 2 × 2 × 3 × 5. This process is crucial because it provides a unique representation of numbers, which is essential in various mathematical applications, including simplifying fractions, finding least common multiples (LCM), and greatest common divisors (GCD).	Numerical Expressions
Definition--Factors and Multiples--Prime Factors	Prime Factors Topic Factors and Multiples Definition Prime factors are the prime numbers that multiply together to give the original number. Description Prime factors are a fundamental concept in the study of factors and multiples. They are the building blocks of all numbers, as any integer greater than 1 can be expressed as a product of prime numbers. This process is known as prime factorization. For example, the prime factorization of 28 is 2 × 2 × 7, where 2 and 7 are prime numbers.	Numerical Expressions
Definition--Factors and Multiples--Proper Factors	Proper Factors Topic Factors and Multiples Definition Proper factors are the factors of a number excluding the number itself and 1. Description Proper factors play a significant role in the study of factors and multiples. Understanding proper factors is essential for grasping more complex mathematical concepts such as prime factorization, greatest common divisors, and least common multiples.	Numerical Expressions
Definition--Factors and Multiples--Simplifying Fractions Using Factoring	Simplifying Fractions with Factoring Topic Factors and Multiples Definition Simplifying fractions involves reducing the fraction to its simplest form by dividing both the numerator and the denominator by their greatest common factor (GCF).	Numerical Expressions
Definition--Factors and Multiples--Unknown Factors	Unknown Factors Topic Factors and Multiples Definition An unknown factor is a value in a multiplication equation that needs to be determined to solve the equation. Description Factors and multiples are fundamental concepts in mathematics, particularly in number theory and arithmetic. Understanding these concepts is crucial for solving a wide range of mathematical problems, from basic arithmetic to more advanced topics such as algebra and number theory. Factors of a number are the integers that can be multiplied together to produce that number. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12. These numbers can be paired in various ways to produce the product 12 (e.g., 2 x 6, 3 x 4).	Numerical Expressions
Definition--Factors and Multiples--Using the LCM to Find a Common Denominator	Using LCM to Find LCD Topic Factors and Multiples Definition The Least Common Multiple (LCM) of two or more numbers is used to find the Least Common Denominator (LCD) when working with fractions.	Numerical Expressions
Definition--Factors and Multiples--Visual Models of Multiples	Visual Models of Common Multiples Topic Factors and Multiples Definition Visual models of multiples are graphical representations that help illustrate the concept of multiples and common multiples of numbers, making it easier to understand their relationships and properties.	Numerical Expressions
Definition--Fraction Concepts--Least Common Multiple (LCM)	Least Common Multiple (LCM) Topic Fractions Definition The Least Common Multiple (LCM) of two or more numbers is the smallest number that is a multiple of each of the numbers. Description The concept of the Least Common Multiple (LCM) is fundamental in the study of fractions. It is particularly useful when adding, subtracting, or comparing fractions. The LCM helps in finding a common denominator, which is essential for performing these operations with fractions.	Fractions and Mixed Numbers
Definition--Least Common Multiple (LCM)	Definition--Least Common Multiple (LCM) This is part of a collection of images that cover key vocabulary on a variety of math topics.	Numerical Expressions and Variable Expressions
Elementary Definition--Multiplication and Division Concepts--Multiple	Multiple Topic Multiplication and Division Definition A multiple is the product of a number and a whole number. Description Multiples are numbers obtained by multiplying a given number by a whole number. For example, the multiples of 3 include 3, 6, 9, 12, and so on. Understanding multiples is crucial for solving problems involving patterns, sequences, and divisibility. They are used in various real-world applications, such as scheduling, where events occur at regular intervals, and in computer science for data organization. Teaching students about multiples helps them identify patterns in numbers and develop their mathematical reasoning skills.	Multiplication Expressions and Equations
INSTRUCTIONAL RESOURCE: Tutorial: Multiples and Factors	INSTRUCTIONAL RESOURCE: Tutorial: Multiples and Factors This tutorial provides an overview of multiples and factors. This includes an exploration of generating multiples by skip-counting. This is part of a collection of math tutorials on a variety of math topics. To see the complete collection of these resources, click on this link. Library of Instructional Resources To see the complete library of Instructional Resources , click on this link.	Complete Number Patterns
Interactive Math Game--Easter Egg (Multiples) Hunt	Interactive Math Game \| Easter Egg (Multiple) Hunt In this Easter Egg hunt, students find the multiples of a given number from a group of eggs with numbers on them. —PRESS PREVIEW TO PLAY THE GAME— This is part of a collection of math games and interactives. To see the complete collection of the games, click on this link. Note: The download is the teacher's guide. Related Resources To see additional resources on this topic, click on the Related Resources tab.	Numerical Expressions
Math Video Definition 26--Multiplication and Division Concepts--Least Common Multiple (LCM)	Math Video Definition 26--Multiplication and Division Concepts--Least Common Multiple (LCM) Topic Multiplication and Division Description The Least Common Multiple (LCM) of two integers is the smallest positive integer that is a multiple of both numbers. For example, the LCM of 2 and 5 is 10. This concept is used in adding fractions and solving problems involving multiples. This term builds on understanding multiples, aiding in fraction operations and problem-solving.	Multiplication Expressions and Equations
Math Video Definition 28--Multiplication and Division Concepts--Multiple	Math Video Definition 28--Multiplication and Division Concepts--Multiple Topic Multiplication and Division Description A Multiple is a product of a number and any whole number. For example, multiples of 2 are 2, 4, 6, 8, and multiples of 3 are 3, 6, 9, 12. Multiples are essential for understanding patterns in arithmetic. This term connects to multiplication concepts, forming a basis for advanced topics like LCM and divisibility.	Multiplication Expressions and Equations
Multiples Table, 1-10	A table that lists all the multiples for the numbers 1-10. Note: The download is a PDF file. Related Resources To see the complete collection of Worksheets on this topic, click on this link: https://bit.ly/3gxcawE	Numerical and Algebraic Expressions
Multiples Table, 1-20	A table that lists all the multiples for the numbers 1-20. Note: The download is a PDF file. Related Resources To see the complete collection of Worksheets on this topic, click on this link: https://bit.ly/3gxcawE	Numerical and Algebraic Expressions
Multiples Table, 1-5	A table that lists all the multiples for the numbers 1-5. Note: The download is a PDF file. Related Resources To see the complete collection of Worksheets on this topic, click on this link: https://bit.ly/3gxcawE	Numerical and Algebraic Expressions
Quizlet Flash Cards: Adding Multiple-Digit Numbers, Set 01	Description In this set of 10 interactive flash cards add numbers with multiple digits. Press the Options button to decide how to display the flash cards. Press the Play button to auto-play the sequence of flash cards. Press Shuffle to change the order of the cards. Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards. Related Resources To see other resources related to this topic, click on the Resources tab above. Quizlet Library To see the complete Quizlet Flash Card Library, click on this Link to see the collection.	Add Multiple-Digit Numbers
Quizlet Flash Cards: Adding Multiple-Digit Numbers, Set 02	Description In this set of 10 interactive flash cards add numbers with multiple digits. Press the Options button to decide how to display the flash cards. Press the Play button to auto-play the sequence of flash cards. Press Shuffle to change the order of the cards. Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards. Related Resources To see other resources related to this topic, click on the Resources tab above. Quizlet Library To see the complete Quizlet Flash Card Library, click on this Link to see the collection.	Add Multiple-Digit Numbers
Quizlet Flash Cards: Adding Multiple-Digit Numbers, Set 03	Description In this set of 10 interactive flash cards add numbers with multiple digits. Press the Options button to decide how to display the flash cards. Press the Play button to auto-play the sequence of flash cards. Press Shuffle to change the order of the cards. Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards. Related Resources To see other resources related to this topic, click on the Resources tab above. Quizlet Library To see the complete Quizlet Flash Card Library, click on this Link to see the collection.	Add Multiple-Digit Numbers
Quizlet Flash Cards: Adding Multiple-Digit Numbers, Set 04	Description In this set of 10 interactive flash cards add numbers with multiple digits. Press the Options button to decide how to display the flash cards. Press the Play button to auto-play the sequence of flash cards. Press Shuffle to change the order of the cards. Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards. Related Resources To see other resources related to this topic, click on the Resources tab above. Quizlet Library To see the complete Quizlet Flash Card Library, click on this Link to see the collection.	Add Multiple-Digit Numbers
Quizlet Flash Cards: Adding Multiple-Digit Numbers, Set 05	Description In this set of 10 interactive flash cards add numbers with multiple digits. Press the Options button to decide how to display the flash cards. Press the Play button to auto-play the sequence of flash cards. Press Shuffle to change the order of the cards. Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards. Related Resources To see other resources related to this topic, click on the Resources tab above. Quizlet Library To see the complete Quizlet Flash Card Library, click on this Link to see the collection.	Add Multiple-Digit Numbers
Quizlet Flash Cards: Dividing by Multiples of 10, Set 01	Description In this set of 10 interactive flash cards divide numbers by multiples of 10. Press the Options button to decide how to display the flash cards. Press the Play button to auto-play the sequence of flash cards. Press Shuffle to change the order of the cards. Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards. Related Resources To see other resources related to this topic, click on the Resources tab above. Quizlet Library To see the complete Quizlet Flash Card Library, click on this Link to see the collection.	Divide by Multiples of 10
Quizlet Flash Cards: Dividing by Multiples of 10, Set 02	Description In this set of 10 interactive flash cards divide numbers by multiples of 10. Press the Options button to decide how to display the flash cards. Press the Play button to auto-play the sequence of flash cards. Press Shuffle to change the order of the cards. Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards. Related Resources To see other resources related to this topic, click on the Resources tab above. Quizlet Library To see the complete Quizlet Flash Card Library, click on this Link to see the collection.	Divide by Multiples of 10
Quizlet Flash Cards: Dividing by Multiples of 10, Set 03	Description In this set of 10 interactive flash cards divide numbers by multiples of 10. Press the Options button to decide how to display the flash cards. Press the Play button to auto-play the sequence of flash cards. Press Shuffle to change the order of the cards. Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards. Related Resources To see other resources related to this topic, click on the Resources tab above. Quizlet Library To see the complete Quizlet Flash Card Library, click on this Link to see the collection.	Divide by Multiples of 10
Quizlet Flash Cards: Dividing by Multiples of 10, Set 04	Description In this set of 10 interactive flash cards divide numbers by multiples of 10. Press the Options button to decide how to display the flash cards. Press the Play button to auto-play the sequence of flash cards. Press Shuffle to change the order of the cards. Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards. Related Resources To see other resources related to this topic, click on the Resources tab above. Quizlet Library To see the complete Quizlet Flash Card Library, click on this Link to see the collection.	Divide by Multiples of 10
Quizlet Flash Cards: Dividing by Multiples of 10, Set 05	Description In this set of 10 interactive flash cards divide numbers by multiples of 10. Press the Options button to decide how to display the flash cards. Press the Play button to auto-play the sequence of flash cards. Press Shuffle to change the order of the cards. Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards. Related Resources To see other resources related to this topic, click on the Resources tab above. Quizlet Library To see the complete Quizlet Flash Card Library, click on this Link to see the collection.	Divide by Multiples of 10
Quizlet Flash Cards: Subtracting Multiple-Digit Numbers, Set 01	Subtract pairs of integers in this 20-flash card set. The integers are in the range -20 to 20. Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards. Related Resources To see the complete collection of Quizlet Flash Cards on this topic, click on this link: https://bit.ly/2XymX2d	Subtract Multiple-Digit Numbers
Quizlet Flash Cards: Subtracting Multiple-Digit Numbers, Set 02	Subtract pairs of integers in this 20-flash card set. The integers are in the range -20 to 20. Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards. Related Resources To see the complete collection of Quizlet Flash Cards on this topic, click on this link: https://bit.ly/2XymX2d	Subtract Multiple-Digit Numbers
Quizlet Flash Cards: Subtracting Multiple-Digit Numbers, Set 03	Subtract pairs of integers in this 20-flash card set. The integers are in the range -20 to 20. Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards. Related Resources To see the complete collection of Quizlet Flash Cards on this topic, click on this link: https://bit.ly/2XymX2d	Subtract Multiple-Digit Numbers
Quizlet Flash Cards: Subtracting Multiple-Digit Numbers, Set 04	Subtract pairs of integers in this 20-flash card set. The integers are in the range -20 to 20. Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards. Related Resources To see the complete collection of Quizlet Flash Cards on this topic, click on this link: https://bit.ly/2XymX2d	Subtract Multiple-Digit Numbers
Quizlet Flash Cards: Subtracting Multiple-Digit Numbers, Set 05	Subtract pairs of integers in this 20-flash card set. The integers are in the range -20 to 20. Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards. Related Resources To see the complete collection of Quizlet Flash Cards on this topic, click on this link: https://bit.ly/2XymX2d	Subtract Multiple-Digit Numbers
Video Definition 21--Primes and Composites--Least Common Multiple (LCM)	Video Definition 21--Primes and Composites--Least Common Multiple (LCM) Topic Prime and Composite Numbers Description Least Common Multiple (LCM): The least common multiple of two integers a and b is the smallest positive integer that is a multiple of both a and b. For example, the LCM of 2 and 5 is 10. The LCM is essential for operations involving fractions, such as finding common denominators.	Prime and Composite Numbers
Video Definition 22--Fraction Concepts--Least Common Multiple (LCM)	Video Definition 22--Fraction Concepts--Least Common Multiple (LCM) Topic Fractions	Fractions and Mixed Numbers
Video Transcript: Percents: Multiple Percents	Video Transcript: Percents: Multiple Percents This is the transcript that goes with the video segment entitled Video: Percents: Multiple Percents. This is part of a collection of video transcripts for the video tutorial series on Percents. To see the complete collection of transcripts, click on this link. Note: The download is a PDF file. Video Transcript Library To see the complete collection of video transcriptsy, click on this link. Video Library To see the complete collection of videos in the Video Library, click on this link.	Percents