GCF vs. LCM

Greatest Common Factor vs. Least Common Multiple

How can you tell if a word problem requires you to use Greatest Common Factor or Least Common Multiple to solve? 

First, use our PROBLEM SOLVING PROCESS

• What do I know?

• What do I need to know?

• What is my plan? 

GCF 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 arrange something into rows or groups

LCM 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. 

Multiple Choice

Example 1

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?

Is this a GCF word problem or an LCM word problem?

• GCF

• LCM

This is a GCF word problem because it requires you to cut the larger pieces into smaller, equal piece. Now, be ready to solve the problem using the GCF!

Fill in the Blanks

Example 1

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?

Type your answer as:

inches

Multiple Choice

Example 2

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?

Is this a GCF word problem or an LCM word problem? Be ready to explain why!

• GCF

• LCM

This is an LCM word problem because it is dealing with events that are happening over and over again and finding when the next time they will both happen will be.

Fill in the Blanks

Example 2

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?

Type your answer as:

days

That is the end of today's lesson! Now it is time to practice!