1. Lesson 2: Greatest Common Factor and Least Common Multiple
Module 1: Arithmetic Operations

2. Table of Contents Introduction: Learning Target 1: Learning Target 2:
I can find the Greatest Common Factor and Least Common Multiple of two whole numbers and use them to solve real-world problems.
Introduction:
I can find the greatest common factor of two whole numbers using upside-down division.
Learning Target 1:
I can find the least common multiple of two whole numbers using upside-down division.
Learning Target 2:
I can identify key words that indicate I need to use GCF or LCM to solve a real-world problem.
Learning Target 3:
I can solve a real-world problem using GCF or LCM.
Learning Target 4:
Culminating:

3. The numbers that are multiplied together in a multiplication problem.
I can find the Greatest Common Factor and Least Common Multiple of two whole numbers and use them to solve real-world problems.
The answer to a multiplication problem.
Introduction to the Lesson Learning Target

4. A number that is greater than zero and is not a decimal or a fraction
I can find the Greatest Common Factor and Least Common Multiple of two whole numbers and use them to solve real-world problems.
Introduction to the Lesson Learning Target

5. By the end of this lesson, you will be able to…
Find the greatest common factor of two whole numbers using upside-down division.
Find the least common multiple of two whole numbers using upside-down division.
Identify key words that indicate GCF and LCM are needed to solve a real-world problem.
Solve real-world problems using GCF and LCM.
By the end of this lesson, you will be able to…

6. The largest factor that is the same for two or more numbers.
I can find the greatest common factor of two whole numbers using upside-down division.
Learning Target 1
The largest factor that is the same for two or more numbers.

7. You’ll know you made a bullseye when…1
You can explain the definition of GCF. 2
You can identify a common factor of two numbers. 3
You can explain how to use upside-down-division 4
You can use upside-down-division to find the greatest common factor of two numbers.
You’ll know you made a bullseye when…

8. Steps for using this tool…
I can find the greatest common factor of two whole numbers using upside-down division. Learning Target 1
Tool Box
The tool I use is…
Steps for using this tool…
What is the tool I use to find the GCF of two whole numbers?
Step 1: Divide both numbers by any common factor.
Step 2: Continue dividing by any common factor until you can only divide by 1.
Step 3: Multiply together only the common factors you divided by.
upside-down Division.

9. #1 2 2
Find the GCF of 12 and 20 1
2 x 2 x 1 = 4
The GCF is 4.

10. #2 3 3
Find the GCF of 18 and 27 1
3 x 3 x 1 = 9
The GCF is 9.

11. #3 2 3
Find the GCF of 24 and 30 1
2 x 3 x 1 = 6
The GCF is 6.

12. I can find the greatest common factor of two whole numbers using upside-down division. Learning Target 1
Keep track of the mistakes you make and turn them into things you learned when finding the GCF of two whole number.
I made a mistake while I was working, but I learned…
GCF should be small (it could be the smaller number).
Cross off the factors at the bottom of the division house. Multiply the factors on the side.
Don’t start by choosing a common factor of one.
Start with small factors if you are getting stuck.
Ask yourself and try, Does 2 work? Does 3 work? Does 4 work? etc…
Don’t forget to add your own!!!

13. Practice on white boards:
I can find the greatest common factor of two whole numbers using upside-down division. Learning Target 1
Practice on white boards:
1.) Find the GCF of 18 and 27.
2.) Find the GCF of 7 and 23.
3.) Find the GCF of 35 and 63.
4.) Find the GCF of 12 and 36.
5.) Find the GCF of 60 and 84. 9 1 7 12 12

14. The smallest multiple that is the same for two or more numbers.
I can find the least common multiple of two whole numbers using upside-down division.
Learning Target 2
The smallest multiple that is the same for two or more numbers.

15. You’ll know you made a bullseye when…1
You can explain the definition of LCM. 2
You can identify a common factor of two numbers. 3
You can explain how to use upside-down-division 4
You can use upside-down-division to find the least common multiple of two numbers.
You’ll know you made a bullseye when…

16. Steps for using this tool…
I can find the least common multiple of two whole numbers using upside-down division. Learning Target 2
Tool Box
The tool I use is…
Steps for using this tool…
What is the tool I use to find the LCM of two whole numbers?
Step 1: Divide both numbers by any common factor.
Step 2: Continue dividing by any common factor until you can only divide by 1.
Step 3: Multiply together all the factors on the outside of the division house.
upside-down division

17. I can find the least common multiple of two whole numbers using upside-down division. Learning Target 2
Keep track of the mistakes you make and turn them into things you learned when finding the LCM of two whole number.
I made a mistake while I was working, but I learned…
LCM should be big (it could be the bigger number).
Multiply all the factors in the BIG L.
Don’t start by choosing a common factor of 1.
Start with small factors if you are getting stuck.
Ask yourself and try, Does 2 work? Does 3 work? Does 4 work? etc…
Don’t forget to add your own!!!

18. #1 1
Find the LCM of 3 and 7
1 x 3 x 7 = 21
The LCM is 21.

19. #2 3 1
Find the LCM of 6 and 9
3 x 1 x 2 x 3 = 18
The LCM is 18.

20. #3 2 1
Find the LCM of 4 and 10
2 x 1 x 2 x 5 = 20
The LCM is 20.

21. Practice on white boards:
I can find the least common multiple of two whole numbers using upside-down division. Learning Target 2
Practice on white boards:
1.) Find the LCM of 5 and 6.
2.) Find the LCM of 8 and 12.
3.) Find the LCM of 7 and 6.
4.) Find the LCM of 5 and 10.
5.) Find the LCM of 2 and 6. 30 24 42 10 6

22. I can find the least common multiple of two whole numbers using upside-down division. Learning Target 2
4-In-A-Row

23. I can identify key words that indicate I need to use GCF or LCM to solve a real-world problem.
Learning Target 3

24. You’ll know you made a bullseye when…1
You are able to identify words that indicate GCF is needed to solve a problem. 2
You are able to identify words that indicate LCM is needed to solve a problem.
You’ll know you made a bullseye when…

25. Will GCF or LCM keep George Banks out of jail?
I can identify key words that indicate I need to use GCF or LCM to solve a real-world problem. Learning Target 3
Will GCF or LCM keep George Banks out of jail?

26. I can identify key words that indicate I need to use GCF or LCM to solve a real-world problem. Learning Target 3
George Banks wants to buy equal amounts of hot dogs and buns. Hot dogs come in packages of 8 and buns come in packages of 12. What is the least amount of hot dogs and buns George Bans will need to buy in order to have equal amounts? Should he use GCF or LCM to solve the problem? Explain your reasoning.

27. Upside-Down-Division
I can identify key words that indicate I need to use GCF or LCM to solve a real-world problem. Learning Target 3
When I hear these
Using this tool
Upside-Down-Division
Equal groups/rows/ sections of...
Greatest/largest number of…
Figuring out how many people can be grouped or receive something.
Find the GCF.

28. Upside-Down-Division
I can identify key words that indicate I need to use GCF or LCM to solve a real-world problem. Learning Target 3
When I hear these
Using this tool
Upside-Down-Division
•Smallest/least amount of…
•…at the same time
•Figuring out how much to buy to have equal amounts.
Find the LCM.

29. I can identify key words that indicate I need to use GCF or LCM to solve a real-world problem. Learning Target 3
GCF or LCM and why?
Dan rides his bike to town every eighth day. Steve walks to town every third day. In how many days will both boys walk to town on the same day?
We would use the LCM because we want to know when something will happen at the same time.

30. I can identify key words that indicate I need to use GCF or LCM to solve a real-world problem. Learning Target 3
GCF or LCM and why?
Twenty-eight girls and 35 boys signed up for the team challenge. Each team needs to have an equal number of girls and boys. What is the greatest number of teams possible?
We would use the GCF because we want break something down into equal groups and fins the greatest number of something.

31. I can solve a real-world problem using GCF or LCM.
Learning Target 4

32. You’ll know you made a bullseye when…1
You are able to use the real-world problem graphic organizer to solve a GCF or LCM problem. 2
You are able to identify if GCF or LCM is needed to solve a real-world problem. 3
You can justify the reasonableness of your answer and explain why it makes sense for the given real-world problem.
You’ll know you made a bullseye when…

33. I can solve a real-world problem using GCF or LCM. Learning Target 4
Keep track of the mistakes you make and turn them into things you learned when finding the GCF of two whole number.
I made a mistake while I was working, but I learned…
To make sure my answer is reasonable.
Don’t forget to add your own!!!

34. I can solve a real-world problem using GCF or LCM. Learning Target 4
In order to be most successful…
Follow all instructions.
Do NOT go ahead.
Pay close attention to detail.
Guided Examples

35. I can solve a real-world problem using GCF or LCM. Learning Target 4
In order to be most successful…
Work together
Stay on task
Be honest with each other.
Group Practice

36. I can find the Greatest Common Factor and Least Common Multiple of two whole numbers and use them to solve real-world problems.
Culminating the Lesson Learning Target

37. By now, you should be able to…
Find the greatest common factor of two whole numbers using upside-down division.
Find the least common multiple of two whole numbers using upside-down division.
Identify key words that indicate GCF and LCM are needed to solve a real-world problem.
Solve real-world problems using GCF and LCM.
By now, you should be able to…

38. Steps for using this tool…
Tool Box
The tool I use is…
Steps for using this tool…

39. When I hear these
Using this tool

40. Keep track of the mistakes you make and turn them into things you learned when _____.
I made a mistake while I was working, but I learned…
_____
Don’t forget to add your own!!!