Real-World GCF and LCM

Solve real-world GCF & LCM math problems! Practice factors, multiples, and critical thinking.

EXPLAIN the difference between factors and multiples, then give an example. Identify whether each question is LCM or GCF. Click on the word problem and choose from the drop-down menu. LCM In how many days will they both be practicing in the gym on the same day? How often do the tours leave at the same time? If both timers just buzzed, how long will it be before both timers buzz again at the same time? If they both start at the same place and time and go in the same direction, how long will it be before they meet again at the starting point? Which caller will be the first to receive both movie tickets and an Applebee’s gift card? In how many days will Mrs. Edwards need to both run and swim on the same day? What is the shortest length at which the two tiles will be the same length? How long will each of their tracks need to be in order for them to be the same length? How many pieces will each boy have used to build their track? GCF What is the greatest number of books Barnes and Noble can pack in each box? What is the largest tile he can use? What is the most the field trip could cost per student? What is the largest number of students that can be invited to the party so that they each get the same amount of chips and water? What is the widest box that will work? If she puts the same number of plants in each row and if each row has only one type of plant, what is the greatest number of plants Mary can put in each row? If one team has 54 points and the other team has 63 points, what is the most points hitting each target can be worth? Real World GCF and LCM 1. The list shows the amounts of money student council collected from students for a field trip. Each student paid the same amount. What is the most the field trip could cost per student?Wednesday $36Thursday $54Friday $72The most the field trip could cost is $18 per student.2. At Subway, the timer for buns buzzes every 11 minutes and the timer for cookies buzzes every 4 minutes. If both timers just buzzed, how long will it be before both timers buzz again at the same time?In 44minutes both buzzers will buzz at the same time.3. Today, both the wrestling team and basketball team were scheduled to have practice in the gym. Whoops! The wrestling team practices in the gym every 4 days and the basketball team practices in the gym every 5 days. In how many days will they both be practicing in the gym on the same day?In 20days they will both be practicing in the gym again.4. Barnes and Noble needs to ship 14 mystery books, 12 science-fiction books, and 8 historical-fiction books. The store can only pack one genre of book in each box, and they must pack the same number of books in each box. What is the greatest number of books Barnes and Noble can pack in each box?Barnes and Noble can put 2books in each box.5. Beginning at 9:00 A.M., tours of the Colosseum and the Vatican begin at a tour agency in Italy. Tours for the Colosseum leave every 8 minutes. Tours for the Vatican leave every 10 minutes. How often do the tours leave at the same time?Every 40minutes the tours will leave at the same time. 6. Bob the Builder is covering the floor with tile. The floor is 18 feet by 27 feet. He wants to use square tiles. What is the largest tile he can use?The largest square tile Bob the Builder can use is 9ft by 9ft.7. Students have just started playing a new game in Mr. Clay’s gym class called Bomb Squad. In the game, you get the same number of points for each target hit. If one team has 54 points and the other team has 63 points, what is the most points hitting each target can be worth?Hitting the target would be worth 9points.8. The sixth grade teachers bought food for a reward party. They purchased 64 bags of chips and 80 bottles of water. What is the largest number of students that can be invited to the party so that they each get the same amount of chips and water?16students can be invited to the reward party.9. Mary Quite Contrary wants to put 45 tomato plants, 81 pepper plants, and 63 corn plants in her garden. If she puts the same number of plants in each row and if each row has only one type of plant, what is the greatest number of plants Mary can put in each row?Mary can put 9plants in each row. 10. Drew has 5 inch pieces of train track and Luke has 7 inch pieces of train track. How long will each of their tracks need to be in order for them to be the same length?Each of their tracks will need to be 35inches in order for them to be the same length.How many pieces will each boy have used to build their track?Drew will have to use 7pieces of track and Luke will have to use 5 pieces of track.