1. 6.NS.4
Compute fluently with multi-digit numbers and find common factors and multiples.

2. 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 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).
Greatest common factor and least common multiple are usually taught as a means of combining fractions with unlike denominators. This cluster builds upon the previous learning of the multiplicative structure of whole numbers, as well as prime and composite numbers in Grade 4. Although the process is the same, the point is to become aware of the relationships between numbers and their multiples. For example, consider answering the question: “If two numbers are multiples of four, will the sum of the two numbers also be a multiple of four?” Being able to see and write the relationships between numbers will be beneficial as further algebraic understandings are developed. Another focus is to be able to see how the GCF is useful in expressing the numbers using the distributive property, ( ) = 12(3+2), where 12 is the GCF of 36 and 24. This concept will be extended in Expressions and Equations as work progresses from understanding the number system and solving equations to simplifying and solving algebraic equations in Grade 7.
Kansas Association of Teachers of Mathematics (KATM) Flipbooks. Questions or to send feedback: Retrieved from:

3. Common Factors
Mrs. Beasley’s class wants to play kick ball. They want to make teams. There are 12 girls and 18 boys.
Describe what the teams can look like.
What questions would you ask about the teams?
What criteria would you set for the teams?
Let students explore!
Facilitate a discussion regarding “teams”
For example, can the class make teams of equal boys and girls? How many teams can they make of equal boys and girls?
If they split the class in half how many students would be on each team?
Does it matter if they have equal boys and girls?
Allow student to ask the rest of the class questions about the teams?
How many people have to be on kickball team?
Allow students to use color counters if a hands on manipulative is needed
Students will be exploring the relationship between numbers.
The final question would probably ask “Can Mrs.Beasley’s class split into two teams with the same amount of boys and girls on each team?”
Will there be any left over students?
This is a great time to talk about the factors of 12, 18 and 30.
Teams could be 2 and 15

4. Greatest Common Factor
Choose two numbers that have two factors of 2 and one factor of 3.
Again allow students to explore
2 x 2 x 3 = 12
And then any multiple of 12 can be the second number – discuss how multiple answers could fit this criteria.
Given the two numbers, talk about the greatest common factor and why it is the greatest common factor.

5. Common Multiples
Kurt goes to tumbling class every 6 days and he goes to story time every 4 days.
When is the first time Kurt will go to both classes? How frequently will this happen in a 60 day period?

6. Least Common Multiple
The school cafeteria serves tacos every sixth day and cheeseburgers every eight day. If tacos and cheeseburgers are both on today’s menu, how many days will it be before they are both on the menu again?

7. Distributive Property
Jim needs to rewrite as a multiple of a sum of two numbers with no common factor. Which of the following are possible solutions?
2 (9 + 15)
3 (6 + 10)
5 ( 3 + 6)
6 ( 3 + 5)
9 ( 2 + 6)

8. Distributive Property
Rewrite the expression as a multiple of a sum of two numbers with no common factor.
Choose 2
2 + 18
33 + 6

9. Word Problem
Lisa is making activity baskets to donate to charity. She has 12 coloring books, 28 markers, and 36 crayons. What is the greatest number of baskets she can make if each type of toy is equally distributed among the baskets? How many of each supply will go into the baskets?
Additional Problems GCF and LCM

10. Finding Least Common Multiple
Describe two different ways to find the least common multiple of 11 and 12?
Listing multiples and multiplying 11 and 12 together since 11 is prime.

11. Greatest Common Factor
I know the greatest common factor of 42 and 6 is 6
Does that mean that the greatest common factor between…
42 and 12 is 12?
42 and 18 is 18?
Explain how you know?

12. Create
Create a word problem that requires the use of greatest common factors, using the numbers 12 and 21.
Students can then discuss their answers in partners, in small groups or whole class

13. Create
Create a word problem that requires the use of greatest common multiples using the numbers 6 and 9.
Students can then discuss their answers in partners, in small groups or whole class

14. Think About???
Typically we find Greatest Common Factors and Least Common Multiples
Is there a situation when you would want to find Least Common Factors and Greatest Common Multiple?
Discuss with a partner.