1. Greatest Common Factor (GCF)
What is a Factor?
What does it mean to have something in common?
1. Use Prime Factorization to get all prime factors (factor trees)
2. Circle the factors that are common
3. Multiply the common factors together to get the “GCF”
Ex: What is the GCF of 6 and 12? 6 12 2 • 3 4 • 3
The GCF of 6 and 12 is __________________. 2 • 2 • 3
Note: 2 and 3 are common factors of 6 and 12. When we multiply them together, we find the Greatest, or largest, common factor.
*Numbers are Relatively Prime if they don’t have any common factors other than 1.
For example, 15 and 32 are relatively prime.

2. Least Common Multiple (LCM)
What is a Multiple?
What does it mean to have something in common?
1. Use Prime Factorization to get all prime factors (factor trees)
2. Multiply all factors, but use common factors only once
3. For a repeating factor, use the one with the highest exponent
Ex: What is the LCM of 20 and 30?
22 • 5 • 3
4 • 5 • 3 = 60
LCM = 60 20 30 2 • 10 10 • 3 2 • 2 • 5 =
22 • 5 2 • 5 • 3 =
2 • • 5
Note: Since 2 is a factor for both 20 and 30, only use the one with the higher exponent value. Use five only once, because it is a common factor.