GCF vs. LCM with LCM Practice

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? 

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!

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.

​Finding LCM for 12 and 10

​List the multiples of each number.

​

​Circle the multiples they have in common or the same.

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​Star the Least or smallest number they have in common or the same.

​Practice

Multiple Choice

What is the first step in finding the LCM?

• Listing the multiples of the numbers

• Listing the factors of the numbers

• Multiplying the numbers by each other

• Dividing the numbers by each other

Multiple Choice

What is the second step in finding the LCM?

• Adding the multiples together

• Finding the average of the numbers

• Finding the biggest multiple

• Identifying which multiples of the numbers that they have in common

Multiple Choice

What is the final step in finding the LCM?

• Adding the multiples together

• Choosing the smallest multiple that the numbers have in common

• Choosing the largest multiple

• Finding the average of the multiples

Multiple Choice

What is the LCM for 6 and 8?

• 6
• 8
• 24
• 48

Multiple Choice

What is the LCM of 2 and 4?

• 4

• 8

• 12

• 16

Multiple Choice

What is the LCM of 3 and 6?

• 3

• 12

• 6

• 18

Multiple Choice

What is the LCM of 5 and 10?

• 5

• 30

• 10

• 20

Multiple Choice

What is the LCM for 4 and 7?

• 4
• 7
• 14
• 28

Multiple Choice

What is the LCM of 8 and 16?

• 24

• 8

• 16

• 32

Multiple Choice

What is the LCM of 3 and 9?

• 27

• 18

• 36

• 9

Multiple Choice

What is the LCM of 6 and 4?

• 24

• 12

• 36

• 48

Multiple Choice

What is the LCM of 5 and 15?

• 30

• 75

• 15

• 45

Multiple Choice

Find the least common denominator. $$\frac{7}{9}\ and\ \frac{1}{6}$$  

• 6

• 9

• 54

• 18

Multiple Choice

John works every 4 days.  Chris works every 7 days.  How many days until they work together again?

• 28
• 11
• 3
• 35

Multiple Choice

Jenny goes to dance class every 6 days, karate class every 12 days, and to the library every 18 days. On December 1st she went to both classes and the library. On what date will she do both classes and go to the library?

• 24 days
• 36 days
• 42 days
• 52 days