GCF and LCM

Greatest Common Factor

And

Least Common Multiple

Problem #1

• A discount store sells two types of marbles. Blue marbles come in bags of 18. Red marbles come in bags of 30. I want to buy the same number of each type of marble.

LCM or GCF

• LCM• How many of each type of marble must

I buy?• How many bags of each type must I

buy?• Predict how many of each type of

marble and how many bags you will purchase.

LCM

• Use a factor tree

• Put prime numbers in order from least to greatest (do not simplify to exponents)

•18 = 2 3 3

•30 = 2 3 5

Winners

•2 x 3 x 3 x 5 = 90

•90 is the LCM for 18 and 30

Back to Problem

• 90 marbles of each type must be purchased

• Blue marbles, 18 per bag – need 5 bags

• Red marbles, 30 per bag – need 3 bags

• Check your prediction!

Problem #2

• You have a bag with 30 green marbles and another bag with 42 yellow marbles. You want to repackage the marbles into smaller bags, and you want each bag to have the same number of each type of marble. You also want as many new bags as you possibly can make.

LCM or GCF

• GCF

• How many of each marble will be in the bags?

• How many bags will you be able to make?

• Will you have any marbles left over?

GCF

• Use a factor tree

• Put prime numbers in order from least to greatest (do not simplify to exponents)

•30 = 2 3 5

•42 = 2 3 7

Partners

•2 x 3 = 6

•6 is the GCF for 30 and 42

Back to Problem

• 6 marbles will go in each bag

• 30 green marbles – 5 bags

• 42 yellow marbles – 7 bags

• No marbles left over!

Assignments

• In Class Assignment:

• Attachment D GCF and LCM

• Homework:

• Attachment C PB Puzzler