GCF and LCM Word Problems

Jeremy has two pieces of wood:  one is 90 inches and the other is 72 inches. He wants to cut both pieces into smaller pieces of the same length.  What is the longest possible length he can cut and not have any lumber left over?

• 9
• 2
• 18
• 72

Tags

CCSS.6.NS.B.4

Melanie has pieces of train track that are 8 inches long that she is connecting together to form a track that her train can travel on. Martin is also trying to construct a track for his train but is using track pieces that are 20 inches long. How long will the shortest track be if the track that Melanie builds ends up being the same length as Martin’s track?

• 10 inches
• 20 inches
• 30 inches
• 40 inches

Tags

CCSS.4.MD.A.2

At the movie theater, they give out a free drink to every 75th customer and a free bag of popcorn to every 30th customer. Who is the first customer that is going to win both free items?

• 16th customer
• 150th customer
• 300th customer
• 180th customer

Tags

CCSS.6.NS.B.4

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

• 24 days

• 36 days

• 42 days

• 52 days

Henry and Margo both began traveling around a circular track. Henry is riding his bike, and Margo is walking. It takes Henry 7 minutes to make it all the way around, and Margo takes 12 minutes. How much time will pass until they meet at the starting line?

• 84 minutes
• 48 minutes
• 854 minutes
• 78 minutes

Tags

CCSS.6.NS.B.4

Two neon signs are turned on at the same time. Both signs blink as they are turned on. One sign blinks every 9 seconds. The other sign blinks every 15 seconds. In how many seconds will they blink together again?

• 48 seconds
• 45 seconds
• 16 seconds
• 8 seconds

Tags

CCSS.6.NS.B.4

Two neon signs are turned on at the same time.  Both signs blink as they are turned on.  One sign blinks every 9 seconds.  The other sign blinks every 15 seconds.  In how many seconds will they blink together?

• Greatest Common Factor
• Least Common Multiple

Tags

CCSS.6.NS.B.4

Peter has 18 oranges, 27 pears, and 12 bananas. He wants to make fruit baskets with the same number of each fruit in each basket. What is the greatest number of fruit baskets he can make? How many of each type of fruit will be in the baskets?

• Greatest Common Factor

• Least Common Multiple

Jeremy has two pieces of wood: one is 90 inches and the other is 72 inches. He wants to cut both pieces of wood into smaller pieces so that all these pieces are the same length. If he wants the pieces to be as long as possible and doesn’t want to have any lumber left over, how long should each piece be? How many total pieces of lumber will he have?

• Greatest Common Factor
• Least Common Multiple

Tags

CCSS.6.NS.B.4

A store is organizing toys into bins. The toys must be put into bins so that each bin contains the same number of toys without mixing the toys.
 What is the greatest number of toys that can be put in a bin?
               Toys to Place in Bins
      Toy                              Number of Toys
Anemones                            12
Limpets                                 14
Snails                                    18

• 1 of each toy 
• 2 of each toy 
• 3 of each toy 
• 4 of each toy 

Tags

CCSS.6.NS.B.4