- 1. Jupiter revolves around the sun every 12 years. Uranus takes 84 years to revolve around the sun. If Uranus and Jupiter passed the same point of the sun sometime in 2002, when will they pass that point together again?
A) GCF
B) LCM
- 2. The sixth-grade classes are competing in a school field day. There are 308 girls and 220 boys who want to participate. Each team must have the same number of girls and the same number of boys. What is the greatest number of teams that can be formed? How many boys and girls will be on each team?
A) LCM
B) GCF
- 3. The middle school band has 60 members. The high school band has 108 members. The bands are going to march once after the other in a parade. The director wants to arrange the bands into the same number of columns. What is the greatest number of columns in which the two bands can be arranged if each column has the same number of marchers? How many band members will be in each column?
A) LCM
B) GCF
- 4. House representatives are elected every two years. The President of the United States is elected every four years. Both were elected in 2004. When is the next year both will be elected?
A) GCF
B) LCM
- 5. A car manual recommends changing the oil every 5,000 miles and inspecting the engine coolant system every 15,000 miles. At how many miles will both be done together for the first time? For the second time?
A) LCM
B) GCF
- 6. 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?
A) LCM
B) GCF
- 7. Ben goes to the gym every 3 days. Isabel goes every 2 days. Assuming they both went on the first of June, how many times did they go to the gym on the same day?
A) LCM
B) GCF
- 8. Sara has 16 red flowers and 24 yellow flowers. She wants to make bouquets with the same number of each color flower in each bouquet. What is the greatest number of bouquets she can make?
A) LCM
B) GCF
- 9. Boxes that are 12 inches tall are being stacked next to boxes that are 18 inches tall. What is the shortest height at which the two stacks will be the same height?
A) LCM
B) GCF
- 10. Lisa is making activity baskets to donate to charity. She has 12 coloring books, 28 markers, and 36 crayons. What is the greatest number of baskets she can make if each type of toy is equally distributed among the baskets? How many of each supply will go into the baskets?
A) GCF
B) LCM
- 11. When Ms. Rand had a dumb Ford Focus, she had to replace the A/C unit every 40,000 miles and replace the tires every 50,000 miles. The car was brand new when Ms. Rand bought it. How many miles did she have on the car when she had to replace both the A/C and tires at the same time? (This is a made up question. Ms. Rand did not hang on to that stupid car for as long as your answer will be. The A/C did go out every 40,000 miles though.) Also, personification is when you give human qualities to an object or animal (example - dumb and stupid car).
A) LCM
B) GCF
- 12. 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?
A) LCM
B) GCF
- 13. PROMOTION In a promotion for a local delicatessen, every eighth customer will get a free sandwich and every sixth customer will get a free drink. Which customer will be first to get both a free sandwich and a free drink?
A) GCF
B) LCM
- 14. 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 doesnt want to have any lumber left over, how long should each piece be? How many total pieces of lumber will he have?
A) GCF
B) LCM
- 15. For football tryouts at a local school, 8 coaches and 84 players will split into groups. Each group will have the same number of coaches and players. What is the greatest number of groups that can be formed? How many coaches and players will be in each of these groups?
A) LCM
B) GCF
- 16. Bridget has swimming lessons every fifth day and diving lessons every third day. If she had a swimming lesson and a dividing lesson on May 5, when will the next date on which she has both swimming and diving lessons?
A) GCF
B) LCM
- 17. A jewelry maker has 24 jade beads and 30 teak beads. What is the greatest number of necklaces she can make? How many beads of each type are on each necklace?
A) LCM
B) GCF
- 18. The marine-life store would like to set up fish tanks that contain equal numbers of angel fish, swordtails, and guppies. What is the greatest number of tanks that can be set up if the store has 12 angel fish, 24 swordtails, and 30 guppies?
A) GCF
B) LCM
- 19. While performing a piece of music, Lesley strikes the cymbals every 6 beats and the triangle is every 8 beats. If she just struck both at the same time, how many beats will pass before she again strikes them at the same time?
A) GCF
B) LCM
- 20. A gift shop wants to make gift baskets for its regular customers. There are 24 bottles of shampoo, 36 tubes of hand lotion, and 60 bars of soap. The same number of each item should be in each basket. What is the greatest number of baskets that can be made?
A) GCF
B) LCM
- 21. Paper cups come in packages of 48. Plastic lids come in packages of 44. What is the smallest number of cups Liam would need to buy to get the same number of cups as lids?
A) GCF
B) LCM
- 22. 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?
A) LCM
B) GCF
- 23. I am planting 50 apple trees and 30 peach trees. I want the same number and type of trees per row. What is the maximum number of trees I can plant per row?
A) GCF
B) LCM
- 24. The school cafeteria serves tacos every sixth day and cheeseburgers every eight day. If tacos and cheeseburgers are both on todays menu, how many days will it be before they are both on the menu again?
A) LCM
B) GCF
- 25. Radio station Z-100 was giving away a $100 bill to every 100th caller during a contest and gave Jingle Ball tickets to every 40th caller. How many callers must call before someone wins both a $100 bill and a Jingle Ball ticket?
A) GCF
B) LCM
- 26. 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 Martins track?
A) GCF
B) LCM
- 27. Luke is waiting for dinner with his family and he is bored. So the waiter gives Luke 36 packets of sugar and 60 packets of artificial sweetener. The waiter wants Luke to divide them into identical groups, with no packets left over, so that the groups can be distributed to some tables at the restaurant. What is the greatest number of groups Luke can make? How many packets of sugar and how many packets of artificial sweetener should be in each group?
A) LCM
B) GCF
- 28. At the movie theater, they give out a free drink to every 75th customer and a free bag of popcorn to every 30th customer. On Monday 3,000 customers came to the theatre. How many people received both free items?
A) GCF
B) LCM
- 29. The science club sponsor is ordering caps and shirts for the boys and girls in the science club. There are 45 science club members. If the caps come in packages of 3 and the shirts come in packages of 5, what is the least number of packages of caps and shirts that will need to be ordered?
A) LCM
B) GCF
- 30. A related example for the usage of the greatest common factor would be tiling rooms. Consider a room with dimensions of 48 x 56 feet. What is the side of the largest square tile which can tile the room?
A) GCF
B) LCM
- 31. Sixty people are invited to a party. There are 24 cups in a package and 18 napkins in a package. What is the least number of packages of cups and napkins that can be bought if each party guest gets one cup and one napkin?
A) GCF
B) LCM
- 32. At Kentucky Fried Chicken, the kitchen staff baked 96 chicken legs, 144 thighs, and 224 wings. The staff had to prepare platters for a catered lunch at an office. Each platter will have the same number of legs, thighs, and wings. How many platters can the staff make if they want the greatest number of chicken pieces on each platter?
A) LCM
B) GCF
- 33. A baker has 36 sesame bagels and 48 plain bagels to put into boxes. Each box must have the same number of each type of bagel. What is the greatest number of boxes that the baker can make using all of the bagels? How many sesame bagels and how many plain bagels will be in each box?
A) GCF
B) LCM
- 34. Grandma takes one medication every six hours. She takes another medication every 12 hours. If she takes both medications at 7 am, when will she take next take both medications at the same time?
A) GCF
B) LCM
- 35. A movie theater runs its films continuously. One move runs for 80 minutes and a second runs for 120 minutes. Both movies begin at 4:00 P.M. When will the movies begin again at the same time?
A) GCF
B) LCM
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