GCF and LCM Review

GCF and LCM Review

​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 the factors they have in common. If there are no

common prime factors, the GCF is 1.

​

OR

​

​1. List all of the possible factors for each number.

​2. Find the biggest number they have in common.

Multiple Choice

A prime number

• has one factor
• has more than 2 factors
• has 100 factors
• has exactly 2 factors: 1 and the number

Multiple Choice

What is the prime factorization of 24?

• 3 x 8
• 3 x 2 x 2 x 2
• 4 x 6
• 2 x 2 x 3

Multiple Choice

What number is a factor for EVERY number?

• 0
• 1
• 2
• 100

​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

​Example

​Find the GCF of 14 and 49.

​

Factors of 14: 2 x 7

Factors 49: 7 x 7

​

7 is the only common factor, so the GCF is 7.

Multiple Choice

What is the GCF of 18 and 24?

• 3
• 6
• 8
• 9

Multiple Choice

What are the factors of 25?

• 1, 2, 3, 5, 10, 15, 25
• 1, 5,  25
• 1, 25
• 1, 5

Multiple Choice

What is the GCF OF 24 and 48?

• 52
• 58
• 24
• 48

Multiple Choice

Find the Greatest  Common Factor (GCF) of 14 & 22.

• 1
• 2
• 7
• 14

Multiple Choice

Find the GCF 24 and 36.

• 8
• 6
• 12
• 4

Multiple Choice

51 is a _____________ of 3

• Factor 
• 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 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:

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

​

Multiples of 4:

4, 8, 12, 16, 20, 24

​

The LCM of 3 and 4 is 12.

​Note the difference between GCF and LCM.

​GCF = biggest number that divides into

both chosen numbers

​

​LCM = smallest number that both

chosen numbers multiply to

Multiple Choice

Find the LCM of 12 and 6. 

• 6
• 12
• 2
• 1

Multiple Choice

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

• 4
• 40
• 15
• 20

Multiple Choice

Find the Least Common Multiple of 9 and 6

• 18
• 36
• 38
• 72

Multiple Choice

What is the least common multiple (LCM) of 2 and 3?

• 6
• 8
• 20
• 10

Multiple Choice

What is the LCM?

• The LCM is the least common factor that both numbers share. 

• The LCM is the biggest multiple that both numbers share.  

• The LCM is the smallest multiple that both numbers share.

• The LCM is the smallest factor that both numbers share.