Lesson Plan: Review of LCM and GCF

Lesson Summary

This 50-minute lesson reviews the concepts of Least Common Multiple (LCM) and Greatest Common Factor (GCF), foundational skills necessary for fraction operations. Students will calculate LCM and GCF for pairs of numbers and apply these skills to fraction operations. Multimedia resources from Media4Math.com will provide interactive and visual learning support. The lesson concludes with a 10-question quiz with an answer key to assess understanding.

Key Vocabulary

Multimedia Resources

 

 

Warm Up Activities

Calculator Activity: Multiples

  1. Provide each student with a calculator.
  2. Assign two numbers, such as 6 and 8.
  3. Ask students to find the multiples of each number up to 50 by repeatedly multiplying the number by integers (e.g., 6, 12, 18, etc.).
  4. Have students write down the multiples and identify the smallest common multiple.
  5. Discuss how this method leads to the LCM.

 

MultiplesMultiples

 

Multimedia Slide Show

  1. Present a slide deck with visuals of number lines and factor trees.
  2. For LCM, show two number lines and highlight multiples of two numbers until the first overlap.
  3. For GCF, display factor trees for pairs of numbers, circling common factors.
  4. Pause after each slide to ask students to identify the LCM or GCF based on the visuals.

 

Multiples of 2 and 3

Multiples

 

Factors of 99

Factors

 

 

Hands-On Activity

  1. Provide students with colored chips or counters.
  2. Assign two numbers, such as 12 and 16.
  3. Have students group the chips into equal sets representing the factors of each number.
  4. Ask students to find the largest group size that divides evenly into both numbers (GCF).
  5. Repeat with multiples to find the smallest group size that matches (LCM).

 

FactorsMultiples

 

 

Teach

Learning to find the LCM and the GCF will help with fraction operations. The first two examples have to do with the LCM and GCF. The third example shows how to use them to add fractions. 

Example 1: Finding LCM

Find the LCM of 6 and 8

  • Step 1: Write multiples of 6 and 8.
    • 6: 6, 12, 18, 24, 30, 36, 42, 48
    • 8: 8, 16, 24, 32, 40, 48
  • Step 2: Identify common multiples and select the smallest.
    • Common Multiples: 24, 48
  • Step 3: The LCM of 6 and 8 is 24.

Example 2: Finding GCF

Find the GCF of 36 and 48.

  • Step 1: Factorize numbers into primes.

36 = 62

= (2 • 3)2

= 22 • 32

48 = 6 • 8

= (2 • 3) • 23

= 24 • 3

  • Step 2: Identify common prime factors.
    • Common factors are 22 • 3
  • Step 3: Multiply common factors. 
    • 22 • 3 = 4 • 3 = 12

The GCF of 36 and 48 is 12.

Example 3: Adding Fractions Using LCM

Add \( \frac{1}{6} + \frac{1}{8} \).

  • Step 1: Find the LCM of the denominators 6 and 8.
    • 6: 6, 12, 18, 24
    • 8: 8: 16, 24
  • Step 2: Multiply the numerator and denominator by the appropriate factor to get a common denominator of 24

 

\( \frac{1}{6} = \frac{1•4}{6•4} \)

= \(\frac{4}{24} \)

\( \frac{1}{8} = \frac{1•3}{8•3} \)

= \(\frac{3}{24} \)

 

  • Step 3: Add fractions: \( \frac{4}{24} + \frac{3}{24} = \frac{7}{24} \).
  • Step 4: Conclude \( \frac{1}{6} + \frac{1}{8} = \frac{7}{24} \).

 

 

Review

This review reinforces key concepts and vocabulary while summarizing the lesson. Students will revisit the importance of LCM and GCF in fraction operations and practice applying these skills. The review also provides worked-out examples to ensure comprehension.

Vocabulary Review

  • LCM: The smallest shared multiple of two or more numbers.
  • GCF: The largest shared factor of two or more numbers.
  • Factor: A number that divides evenly into another number.
  • Multiple: The product of a given number and any integer.

Example 1: Simplifying a Fraction Using GCF

Simplify \(\frac{48}{64}\).

  • Step 1: Find the GCF of 48 and 64. 

48 = 6 • 8

= 2 • 3 • 23

= 24 • 3

64 = 82

= (23)2

= 26

  • Step 2: The GCF is 24 = 16.
  • Step 3: Divide the numerator and denominator by 16: \(\frac{48}{64} = \frac{3}{4}\).
  • Step 4: Conclude that \(\frac{48}{64}\) simplifies to \(\frac{3}{4}\).

Example 2: Adding Fractions with Different Denominators

Add \(\frac{5}{12} + \frac{7}{18}\).

  • Step 1: Find the LCM of 12 and 18. 
    • 12: 12, 24, 36, 48, 60, 72
    • 18: 18, 36, 54, 72
  • Step 2: The LCM is 36.
  • Step 3: Rewrite the fractions: 

 

\(\frac{5}{12} = \frac{5•3}{12•3}\)

= \(\frac{15}{36}\)

\(\frac{7}{18} = \frac{7•2}{18•2}\)

= \(\frac{14}{36}\)

 

  • Step 4: Add the fractions: \(\frac{15}{36} + \frac{14}{36} = \frac{29}{36}\).
  • Step 5: Conclude that \(\frac{5}{12} + \frac{7}{18} = \frac{29}{36}\).

This summary and these examples solidify understanding by modeling the application of LCM and GCF in solving fraction problems.

Multimedia Resources

 

 

Quiz

Directions: Answer the following. Show work where needed.

  1. List factors of 24 and 36. Identify the GCF.
  2. Find LCM of 5 and 7.
  3. Find GCF of 32 and 48 using prime factorization.
  4. Calculate LCM for 4 and 10.
  5. Simplify \( \frac{12}{16} \) using GCF.
  6. Add \( \frac{1}{4} + \frac{1}{6} \) (find the LCM first).
  7. Find GCF of 18 and 27.
  8. What is the LCM of 9 and 15?
  9. Suppose you are adding two fractions, one with a denominator of 8 and the other with a denominator of 12. Use the LCM to find a common denominator.
  10. Simplify the fraction \( \frac{18}{27} \) using the GCF.

Answer Key

  • Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24. Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36. GCF: 12.
  • LCM of 5 and 7: 35.
  • Prime factorization of 32: 2 x 2 x 2 x 2 x 2. Prime factorization of 48: 2 x 2 x 2 x 2 x 3. GCF: 16.
  • LCM of 4 and 10: 20.
  • Simplify \( \frac{12}{16} \): \( \frac{3}{4} \).
  • LCM of 4 and 6: 12. \( \frac{1}{4} = \frac{3}{12} \), \( \frac{1}{6} = \frac{2}{12} \), Sum: \( \frac{5}{12} \).
  • GCF of 18 and 27: 9.
  • LCM of 9 and 15: 45.
  • LCM of 8 and 12: 24. Common denominator: 24.
  • Prime factorization of 18: 2 x 3 x 3. Prime factorization of 27: 3 x 3 x 3. GCF: 9. Simplify: \( \frac{18}{27} = \frac{2}{3} \).