1. Greatest Common Factor and Least Common Multiple
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2. Warm Up
Find the LCM.
4, 12
9, 12
7, 8, 14
3, 4, 5 12 36 56 60

3. Example 1: Find the LCM of 15, 18, and 20.
You can find the LCM using prime factorization.
Write the prime factorizations. Find all of the different factors where they appear the most number of times.
15 = 3 x 5
18 = 2 x 3 x 3
Multiply the factors.
5 x 3 x 3 x 2 x 2 = 180
20 = 2 x 2 x 5
The LCM is 180.

4. Example 2:
Mom is creating snack bags for a trip. She has 6 bags of chips and 10 packs of crackers. She wants each snack bag to have the same amount of each. What is the greatest number of snack bags mom can make with no snacks left over?
Find the GCF of 6 and 10.
The GCF of 6 and 10 is 2.
Mom can make 2 snack bags with 3 bags of chips and 5 packs of crackers.

5. Example 3
Kim is packing equal numbers of grapes and pretzels for snacks. Kim bags the grapes in groups of 18 and the pretzels in groups of 9. What is the smallest number of grapes and pretzels she can pack?
Find the LCM of 18 and 9.
The LCM of 18 and 9 is 18.

6. Example 4:
The GCF of two numbers less than or equal to 12 is 4. Their LCM is 24. What are the two numbers?
8 and 12
The GCF of 8 and 12 is 4 and the LCM is 24.

7. What is the least common factor of any pair of numbers?
Closure
What is the least common factor of any pair of numbers? 1