GCF and LCM

GCF and LCM

How to find the Greatest Common Factor and Least Common Multiple

Greatest Common Factors

Multiple Choice

Which pair of numbers has a GCF of 5?

• 10 and 25
• 30 and 40
• 45 and 9
• 50 and 25

Multiple Choice

Find the GCF of 64 and 144.

Hint-Remember to use your factor trees to help you.

• 8

• 6

• 16

• 2

How to Find the Greatest Common Factor (GCF)

The Greatest Common Factor, or GCF, is the greatest factor that divides two numbers. To find the GCF of two numbers:

1. List the prime factors of each number.

2. Multiply those factors they both have in common. If there are no common prime factors, the GCF is 1.

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GCF continued

Prime Factors of 18: 2 x 3 x 3

Prime Factors of 24: 2 x 2 x 2 x 3

There is one 2 and one 3 in common.

The GCF is 2 x 3 = 6

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Example

Find the GCF of 14 and 49F

Factors of 14: 2 x 7

Factors 49: 7 x 7

7 is the only common factor. Therefore the GCF is 7

Least Common Multiple

Least Common Multiple (LCM)

A common multiple is a number that is a multiple of two or more numbers. The common multiples of 3 and 4 are 0, 12, 24, ....

The least common multiple (LCM) of two numbers is the smallest number (not zero) that is a multiple of both.

Least Common Multiple

Multiples of 3:

0, 3, 6, 9, 12, 15, 18, 21, 24

Multiples of 4:

0, 4, 8, 12, 16, 20, 24

The LCM of 3 and 4 is 12

Multiple Choice

What is the least common multiple (LCM) of 4 and 10?

• 4
• 40
• 15
• 20

Multiple Choice

What number is a factor for EVERY number?

• 0
• 1
• 2
• 100

Multiple Choice

What is the least common multiple (LCM) of 4 and 10?

• 4
• 40
• 15
• 20

Multiple Choice

Which is a NOT a factor of 9?

• 0
• 1
• 3
• 9

Multiple Choice

What is the GCF of 7 and 18?

• 7
• 18
• 1
• 3

Multiple Choice

51 is a _____________ of 3

• Factor 
• Multiple

Multiple Choice

Pencils come in packs of 8 and highlighters in packs of 12.  
A.  What is the least number of pencils and highlighters you need to buy for an equal amount?
B.  What is the least number of packages you need to buy to have an equal amount of pencils and highlighters?

• A. 4  B.  2 pencil and 3 highlighter
• A.  48  B.  6 pencil and 4 highlighter
• A. 24  B. 3 pencil and 2 highlighter

Multiple Choice

Bill cut out 6 squares and 8 circles. He divided the cutouts into groups so that the same number of squares and circles were in each group. What is the greatest number of groups he could have made?

• 2

• 3

• 4

Multiple Choice

List all the factors of 12

• 1, 2, 3, 4, 6, 12
• 1, 2, 4, 12
• 1, 12
• 1, 2, 3, 4, 5, 6, 12