1. The ABC’s of GCF and LCM

2. GCF = Greatest Common Factor
If the word factor is in the name, I know this has to do with multiplication.
Greatest obviously means the factor with the largest value
Common must mean more than one number has this single factor

3. Greatest Common Factor
The Greatest Common Factor is the largest factor two or more numbers share
How do you find the GCF of 12 and 18?
Using the rules of divisibility, find all of the factors of 12 and 18
12= 1, 2, 3, 4, 6, 12
18 = 1, 2, 3, 6, 9, 18

4. Greatest Common Factor
12= 1, 2, 3, 4, 6, 12
18 = 1, 2, 3, 6, 9, 18
Find the numbers that occur in both lists
Choose the number that is the largest
The Greatest Common Factor of 12 and 18 is 6

5. Greatest Common Factor
Find the GCF between 75 and 30
Use the rules of divisibility to help you
75 –ends in * 15
- digits add to 12 (which is divisible by 3) * 25
- follows the identity property * 75
The factors of 75 are 1, 3, 5, 15, 25, 75

6. Greatest Common Factor
Find the GCF between 75 and 30
Use the rules of divisibility to help you
30 –ends in 5 and * 6
3 * 10
- is an even number * 15
- follows the identity property * 30
The factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30

7. Greatest Common Factor
Compare the two strings of factors and find the largest common factor:
75 = 1, 3, 5, 15, 25, 75
30 = 1, 2, 3, 5, 6, 10, 15, 30
The Greatest Common Factor is 15

8. Greatest Common Factor and Factor Trees
Create factor trees for 18 and 30- remember to divide down to the prime factorization of each number
3 * * 6
3 * *2
3*3* * 3 * 2

9. Greatest Common Factor and Factor Trees
3 * * 6
3 * *2
3*3* * 3 * 2
3 and 2 are common in both prime factorization, therefore 3*2 or 6 is the GCF

10. Practice Time
Math Journal 2 page
Math Practice Book 13.2

11. Least Common Multiple
If the word multiple is in the name, I know this has to do with multiplication
A multiple is the product of two numbers that are multiplied together
7*3 = is the multiple of 7 and 3
Least means I am looking for the smallest multiple
Common means the multiple must be included in both numbers multiple strings

12. Least Common Multiple Find the Least Common Multiple of 4 and 6
List the multiples in order for each number:
4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48…
6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72…
What is the smallest number that sits in both strings?

13. Least Common Multiple Find the Least Common Multiple of 4 and 6
List the multiples in order for each number:
4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48…
6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72…
What is the smallest number that sits in both strings?

14. 6 and 8 3 and 8 6 and 9 24 24 18 Least Common Multiple
Find the LCM of:
6 and and and 9

15. Practice LCM
Math Practice Book 13.3

16. Using Factor Trees to find the LCM
Use factor trees to find the prime factorization for 18 and 30
3 * * 6
3 * *2
3*3* * 3 * 2
3*2 repeats in both factor strings

17. Using Factor Trees to find the LCM
3*3* * 2 * 5
3*2 repeats in both factor strings
Eliminate one set of 3 * 2 and multiply the rest of the prime factors together
3 * 3 * 2 * 5 90
The LCM of 18 and 30 is 90

18. Greatest Common Factor and Factor Trees
3 * * 6
3 * *2
3*3* * 3 * 2
3 and 2 are common in both prime factorization, therefore 3*2 or 6 is the GCF

19. Factoring out the LCM
Find the LCM using factor tree method for:
12 and and and 24

20. Factoring out the LCM
Practice this method
Math Journal 2 page 408