GCF vs. LCM Lesson

GCF vs. LCM

Thursday 3/2/23

Greatest Common Factor (GCF) Word Problems May Be Asking You:

• To split things into smaller sections

• To equally distribute 2 or more sets of items into their largest grouping

• To find how much of each item will be in each group (using the GCF to answer the question… that means that the GCF is NOT your answer)

Least Common Multiple (LCM) Word Problems May Be Asking You:

• About an event that is or will be repeating over and over

• To purchase or get multiple items in order to have enough

• To figure out when something will happen again at the same time

Next, you will try some on your own!

You will have two tasks with this:

1. Read through the problem. Then determine if the GCF or LCM will be used to solve the problem. Be sure to explain why.

2. Use the GCF or LCM to solve the problem.

Open Ended

Samantha has two pieces of cloth.  One piece is 72 inches wide and the other piece is 90 inches wide.  She wants to cut both pieces into strips of equal width that are as wide as possible.  How wide should she cut the strips?

Will the GCF or LCM be used to answer this question? Explain your reasoning.

Samantha has two pieces of cloth.  One piece is 72 inches wide and the other piece is 90 inches wide.  She wants to cut both pieces into strips of equal width that are as wide as possible.  How wide should she cut the strips?

This problem can be solved using the GCF because Samantha is cutting (splitting) each piece of cloth into smaller pieces (just like how factors are smaller than the original number).  She also wants the strip to be as wide (or large) as possible.

​Samantha has two pieces of cloth.  One piece is 72 inches wide and the other piece is 90 inches wide.  She wants to cut both pieces into strips of equal width that are as wide as possible.  How wide should she cut the strips?

72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72

90: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90

The GCF is 18.  So the strips can be cut into 18 inch pieces.

Open Ended

Ben exercises every 12 days and Isabel every 8 days.  Ben and Isabel both exercised today.  How many days will it be until they exercise together again?

Will the GCF or LCM be used to answer this question? Explain your reasoning.

Ben exercises every 12 days and Isabel every 8 days.  Ben and Isabel both exercised today.  How many days will it be until they exercise together again?

This problem can be solved using the LCM because Ben and Isabel are repeating an event multiple times to see when they will meet at the same time again.  Since time continues on, you need to list out the multiples of the number of days they work out to see the earlier time they will work out again together.

Ben exercises every 12 days and Isabel every 8 days.  Ben and Isabel both exercised today.  How many days will it be until they exercise together again?

12: 12, 24, …

8: 8, 16, 24, …

The LCM is 24.  So, Ben and Isabel will exercise together again in

24 days.

​

Now, flip to the back of your notes sheet and complete the

3 You Try Problems!