1. Greatest Common Factors (GCF)

2. Vocabulary Factor Greatest Common Factor
The numbers multiplied together to get a product.
Greatest Common Factor
The largest factor that is the same between two numbers.
Example:
Factors of 4: 1, 2, 4
Factors of 12: 1, 2, 3, 4, 6, 12
The GCF is 4.

3. Ladder Method For GCF Write both numbers on the same line Draw an “L”
Divide the same number into the numbers inside the “L”
Continue to divide into the numbers until you can’t anymore
Multiply the numbers down the LEFT side
This is your GCF
Video:

4. Let’s try some together. Find the GCF.
16 and 24
9 and 29
20 and 45
12, 16, and 24

5. Let’s try some together.
Pg. 8: 1a. Lana earned $49 on Friday, $42 on Saturday, and $21 on Sunday selling bracelets. She sold each bracelet for the same price. What is the most she could have charged for each bracelet?
Warren has 60 carrot sticks and 42 celery sticks. He wants to package them in plastic bags so that each bag has an equal number of carrot and celery sticks. What is the greatest number of bags he can put together?

6. Marker board practice Find the GCF.
4 and 12
6, 8, and 42
9 and 19

7. Marker board practice
Betty has 24 pieces of gum and 30 pieces of candy. She wants to package them in bags so that each bag has the same number of gum and candy in each. What is the greatest number of bags she can put together?
Jackie earned $36 on Monday, and $48 on Tuesday from selling brownies. Each brownie cost the same. What is the most she could have charged for each brownie?

8. Complete
p. 10: 1, AND
p. 11: 1 and 9

9. Least Common Multiple (LCM)

10. Vocabulary Multiple Least Common Multiple
The product of the number and any nonzero whole number
Least Common Multiple
The smallest multiple that is the same between two numbers.
Example:
Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32
Multiples of 12: 12, 24, 36, 48

11. Ladder Method For LCM Write both numbers on the same line Draw an “L”
Divide the same number into both numbers inside the “L”
Continue to divide into the numbers until you can’t anymore
Multiply the numbers down the LEFT AND BOTTOM
This is your LCM
Video:

12. Let’s try some together. Find the LCM.
5 and 2
12 and 8
9 and 3
9 and 21

13. Let’s try some together.
Pg 10: 5. Ernesto has a painting class every 2 weeks. Kamala has a pottery class every 5 weeks. Ernesto and Kamala met at the art building for class this week. How many weeks will it be until they see each other again?
Pg 11: 7. The Movie House gives away a $5 coupon for every 4 movies purchased. They give away a bag of popcorn for every 3 movies purchased. How many movies would you have to purchase in all before receiving both things?

14. Marker Board Problems Find the LCM.
5 and 15
3 and 6
12 and 24
14 and 28

15. Marker board problems
At the grand opening of a store, every 6th customer to enter the store is given a $10 gift certificate and every 9th customer is given a coupon for 10% off their total purchase. Which customer is the first to receive both gifts?
Jay has karate evaluations every 3 weeks. His sister Jamie has dance competition every 5 weeks. Today, Jay had a karate evaluation and Jamie had a dance competition. How many weeks will it be before this happens again?

16. Finding the LCM of 3 or more numbers
Put the numbers in the ladder as before.
When you can NO longer divide into ALL numbers with the SAME divisor, STOP!
This will be your GCF, multiply the numbers down the LEFT side.
To find the LCM, continue to divide UNTIL you have ALL prime numbers and/or 1’s.
If the divisor does NOT go into one of the numbers, simply BRING IT DOWN!
You also can NOT have any duplicate numbers.
Divide by the duplicate numbers to get rid of them.

17. Example 14 20 30 28 7 does not go into 2 or 3, just BRING THEM DOWN!
5 does not go into 7 or 14 , just BRING THEM DOWN!
7 does not go into 2 or 3, just BRING THEM DOWN!
There are duplicate 2’s, so divide by 2 to get rid of them—2 doesn’t go into 1 or 3, so just bring them down.