The Algebra Teacher\'s Guide to Reteaching Essential Concepts and Skills

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WORKSHEET 1.12: FINDING THE LEAST COMMON MULTIPLE

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The least common multiple (LCM) is the smallest number that is a multiple of two or more

numbers. To find the LCM of two numbers, do the following:

1. Write the prime factorization of each number.


2. Find the product of each prime number raised to the largest power.

EXAMPLE

Find the LCM of 24 and 180.

24 = 23 × 3 180 = 22 × 32 × 5

In the prime factorization of 24 and 180, the largest power of 2 is 23 and the largest power

of 3 is 32 .Theonlypowerof5is 51 , which is 5. The LCM of 24 and 180 is 23 × 32 × 5 = 360.

DIRECTIONS: Find the LCM of each pair of numbers.

1. 15, 12 2. 20, 24 3. 16, 10 4. 45, 48


2. 27, 36 6. 18, 90 7. 25, 75 8. 64, 28


3. 115, 15 10. 6, 80 11. 4, 24 12. 11, 130

CHALLENGE:Do you agree with the following statement? If two numbers

have no common factor other than 1, then their product is the LCM. Explain

your answer.

25

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2011 by Judith A. Muschla, Gary Robert Muschla, and Erin Muschla. All rights reserved.