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**Finding the Greatest Common Factor**

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The greatest common factor of two or more numbers is the greatest number that is a factor of every number.

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**There are two methods for finding the GCF. 1. Listing the factors 2**

There are two methods for finding the GCF Listing the factors 2. Using the Ladder

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To find the GCF of two numbers using a list, list the factors of one number. Then list the factors of the second number. The GCF is the greatest value that appears on both lists.

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**1. Make a list to find the GCF of 18 and 30 18: 1, 2, 3, 6, 9, 18 30: 1, 2, 3, 5, 6, 10, 15, 30**

THE GCF of 18 and 30 is 6.

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To find the GCF of two numbers using the ladder method, determine a prime number that you can divide evenly into each number. Write the number on the side and divide. Continue as far as you can!

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**2. Use a ladder to find the GCF of 27 and 36**

3 x 3 =9 so the GCF is 9 3 9 12 3 4

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**Finding the Least Common Multiple**

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The Least Common Multiple of two or more numbers is the smallest number that is a multiple of every number.

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**Listing the multiples Using the Ladder**

There are two methods for finding the LCM. Listing the multiples Using the Ladder

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To find the LCM of two numbers using a list, list the first ten multiples of one number. Then list the first ten multiples of the second number. The LCM is the smallest value that appears on both lists. (You might need to add more than the first ten multiples of each number)

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**Make a list to find the LCM of 6 and 15.**

6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60 15: 15, 30, 45, 60, 75, 90, 105, 120, 135, 150

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To find the LCM of two number using the ladder method, determine a number that you can divide evenly into each number. Write the number on the side and divide. Continue as far as you can!

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**Use the ladder method to find the LCM of 27 and 36.**

3 4 3x3x3x4 = 9 x 12= 108

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**Use the ladder method to find the LCM of 20 and 24.**

20 24

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**Use the ladder method to find the LCM of 9 and 12.**

9 12

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**Use the ladder method to find the LCM of 8 and 6.**

8 6

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© Boardworks 20101 of 13 Unit 1 – Number Systems GCF and LCM.

© Boardworks 20101 of 13 Unit 1 – Number Systems GCF and LCM.

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