1. Greatest Common Factor (GCF and Least Common Multiple (LCM)
Presented by Mr. Laws
6th Grade Math
JCMS

2. Goal/Standard
6.NS.4 - Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12.
Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express as 4 (9 + 2).
Tip: Add your own speaker notes here.

3. Essential Question:
How do I find the GCF and LCM of two whole numbers? (Part I)
How do I find the GCF using the Distributive Property? (Part II)
Tip: Add your own speaker notes here.

4. Distributive Property Greatest Common Factor
Key Vocabulary
Distributive Property
Factors
Greatest Common Factor
Least Common Multiple
Multiples
Prime Factorization

5. Greatest Common Factor (GCF)
A factor is a number that can be multiplied by another number to get a product. Ex. Factor of 10: 1 x 10, 2 x 5
The Greatest Common Factor (GCF) is the largest common factor of two or more given numbers.

6. How Do I Find the GCF? Sample problem # 1 Find the GCF of 20 and 50.
Step 1: List factors of 20
Ex. {1 x 20; 2 x 10; 4 x 5;
5 x 4; 10 x 2; 20 x 1}
Factors of 20:
1, 2, 4, 5, 10, 20
Factors of 50:
Step 2: List factors of 50
Ex. {1 x 50; 2 x 25; 5 x 10, 10 x 5; 25 x 2; 50 x 1}
1, 2, 5, 10, 25, 50

7. How Do I Find the GCF? Sample problem # 1 Find the GCF of 20 and 50.
Step 3: Identify factors that appear in both list. What are they?
Factors of 20:
1, 2, 4, 5, 10, 20
Factors of 50:
Step 4: Identify the greatest common factor (GCF)
1, 2, 5, 10, 25, 50
The GCF of 20 and 50 is 10. Why?

8. Least Common Multiple (LCM)
3. A multiple is the product of a number and any counting numbers.
Ex. Multiples of 4 : [4, 8, 12, 16, 20, 24…etc.}
4. The least common multiple (LCM) is the smallest number, other than zero, that is a multiple of two or more given numbers.

9. How do I find the LCM Sample problem # 2 Find the LCM 8 and 12
Step 1: List the multiples of 8
Multiples of 8:
8, 16, 24, 32, 40, 48
Multiples of 12:
Step 2: List the multiples of 12
12, 24, 36, 48, 60, 72
What are the multiples that appear on both list?

10. How do I find the LCM? Sample problem # 2 Find the LCM 8 and 12
Step 3 Identify multiples that appear in both list.
Multiples of 8:
8, 16, 24, 32, 40, 48
Multiples of 12:
Step 4: What is the least common multiple? Why
12, 24, 36, 48, 60, 72

11. How do I find the LCM? Sample problem # 2 Find the LCM 8 and 12
Step 3 Identify multiples that appear in both list.
Multiples of 8:
8, 16, 24, 32, 40, 48
Multiples of 12:
Step 4: What is the least common multiple? Why
12, 24, 36, 48, 60, 72
Answer: The LCM of 8 and 12 is 24

12. Using the Distributive Property
5. The Distributive Property can be used to write the sum of two numbers another way.
a(b + c) = ab + ac
2(4 + 6) = (2 x 4) + (2 x 6)
2(10) =
20 = 20

13. Using the Distributive Property
6. The distributive property lets you multiply a sum by multiplying each addend separately and then add the products.

14. EQ: How do I find the GCF using the Distributive Property?
Sample Problem # 3
Using the GCF and Distributive Property, write an equivalent of expression of
Step 1 Find the GCF for 56 and 64 a
GCF = 8
8 ( 7 + 8) = (8 x 7) + (8 x 8)
8 ( 15) =
120 = 120
Step 2 Use the GCF (8) and the distributive property to rewrite the sum .
The sum of can be written as 8( 7 + 8)

15. How do I find use prime factorization to find the greatest common factor?
Sample Problem # 4
Find the GCF of 24 and 40
Step 1. Draw a Factor Tree to show prime factorization. Prime factorization is a way to write a number as a product of prime numbers.
Step 2. Multiply the GCF number by the repeating prime numbers to get the GCF.
(Note: prime numbers are natural numbers or positive integer that is not divisible without remainder by any integer except itself and 1, with 1 often excluded)
GCF is 2 x 2 x 2 = 8

16. How do I find the LCM and GCF using the Ladder Method?
Sample Problem # 5
Find the LCM and GCF of 24 and 36 2
Step 1. Find the smallest prime number that can go in 24 and 36. Draw a L under the numbers. x 2 x
6 9 3
Step 2. Find the smallest prime number that can go in 12 and 18. Draw a L under the numbers.
2 3 x
GCF is 2 x 2 x 3 = 12
Step 3. Find the smallest prime number that can go in 6 and 9. Draw a L under the numbers.
LCM is 2 x 2 x 3 x 2 x 3= 72

17. How do I find the LCM and GCF using the Ladder Method?
Sample Problem # 5
Find the LCM and GCF of 24 and 36 2
Step 4. Draw a L on the outside of the prime numbers. x 2 x
Step 5. Multiply the side prime numbers to get the GCF. (2 x 2 x 3 = 12)
6 9 3
2 3 x
Step 6. Multiply the GCF number by the other prime numbers to get the LCM. (2 x 2 x 3 x 2 x 3 = 72)
GCF is 2 x 2 x 3 = 12
LCM is 2 x 2 x 3 x 2 x 3= 72

18. Summary What have you learned about this lesson?
What are some important steps to remember when finding the GCF and LCM?
Do you have any more questions about this lesson?
Make sure you review your notes, add additional questions or notes, and write a summary or reflection.