1. Topic #3: GCF and LCM
What is the difference between a factor and a multiple?
List all of the factors and the first 3 multiples of 6.

2. Example: Find the GCF of 6 and 21.
The GCF is 3.
Example: Find the LCM of 6 and 21.
The LCM is 42.

3. When looking for the GCF of terms with variables, choose the smallest power of each variable.
Example: Find the GCF of x5 and x3.
The GCF is x3.

4. When looking for the LCM of terms with variables, choose the largest power of each variable.
Example: Find the LCM of x5 and x3.
The LCM is x5.

5. Find the GCF and LCM
6x and 3
GCF = LCM = 6x

6. Find the GCF and LCM
12x and 15xy
GCF = 3x LCM = 60xy

7. Find the GCF and LCM
10x2y and 15xy2
GCF = 5xy LCM = 30x2y2

8. How will you remember the difference between a GCF and an LCM?

9. Find the GCF and LCM 2 and 6 GCF = 2 LCM = 6 3 and 4 GCF = 1 LCM = 12

10. Find the GCF of 3xy3 and 15x4y2.
Find the LCM of 3xy3 and 15x4y2.

11. GCF and LCM
Greatest Common Factor (GCF) – the GCF of two numbers is the biggest factor they have in common.  In other words, the biggest number that divides evenly into both numbers.
Example: Find the GCF of 6 and 21.
Factors of 6: 1, 2, 3, 6
Factors of 21: 1, 3, 7, 21
GCF is 3.

12. GCF and LCM
Least Common Multiple (LCM) – the smallest multiple that two or more numbers have in common. 
Example: Find the LCM of 6 and 21.
Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48…
Multiples of 21: 21, 42, 63…
LCM is 42.