LCM and GCF word problems

Peter has 18 oranges and 27 pears. 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?

• 1

• 2

• 3

• 4

Answer explanation

To find the greatest number of baskets, determine the GCD of 18 and 27. The GCD is 9. Thus, Peter can make 18/9 = 2 baskets of oranges and 27/9 = 3 baskets of pears. The limiting factor is 2 baskets, but he can make 3 baskets total.

Jenny goes to  karate class every 12 days.and too 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

Answer explanation

To find when Jenny will do both activities again, calculate the least common multiple (LCM) of 12 and 18. The LCM is 36 days. Thus, she will go to both the karate class and the library again on December 1st + 36 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

Answer explanation

To find when Henry and Margo meet at the starting line, calculate the least common multiple (LCM) of their times: LCM(7, 12) = 84 minutes. Thus, they will meet at the starting line after 84 minutes.

Peter has 18 oranges and 27 pears. He wants to make fruit baskets with the same number of each fruit in each basket. How many PEARS will be in the greatest number of fruit baskets?

• 7

• 8

• 9

• 10

Answer explanation

To find the greatest number of baskets with the same number of pears, we need the greatest common divisor (GCD) of 18 and 27. The GCD is 9, so each basket can contain 9 pears, allowing for 2 baskets.

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

Answer explanation

To find the first customer who wins both items, we need the least common multiple (LCM) of 75 and 30. The LCM is 150, meaning the 150th customer will receive both a free drink and a free bag of popcorn.

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

Answer explanation

To find the shortest track length that Melanie and Martin can both achieve, we need the least common multiple (LCM) of 8 and 20. The LCM is 40 inches, which means both can build tracks of this length.

Kiara baked 30 oatmeal cookies and 48 chocolate chip cookies to package in plastic containers
for her teacher friends at school. She wants to divide the cookies into identical containers so that each
container has the same number of each kind of cookie. If she wants each container to have the
greatest number of cookies possible, how many plastic containers does she need?

• 2

• 4

• 6

• 8

Answer explanation

To find the greatest number of identical containers, we need the greatest common divisor (GCD) of 30 and 48. The GCD is 6, meaning Kiara can use 6 containers, with each containing 5 oatmeal and 8 chocolate chip cookies.

There are 48 girls and 64 boys. 
The choir teacher plans to arrange the students in equal rows.
Only girls or boys will be in each row (no mixing of girls and boys in the same row). What is the greatest number of students that could be in each row?

• 8

• 6

• 16

• 12

Answer explanation

To find the greatest number of students per row, we need the greatest common divisor (GCD) of 48 (girls) and 64 (boys). The GCD is 16, meaning the maximum number of students in each row, without mixing genders, is 16.

There are 40 girls and 32 boys who want to participate in 6th grade intramurals. If each team must
have the same number of girls and the same number of boys. What is the greatest number of teams that can participate in intramurals?

• 6

• 4

• 8

• 2

Answer explanation

To find the greatest number of teams, divide the number of girls (40) and boys (32) by the same number. The GCD of 40 and 32 is 8. Each team can have 5 girls and 4 boys, allowing for 4 teams (40/5 = 8 and 32/4 = 8). Thus, the answer is 4.

Shannon is making identical balloon arrangements for a party. She has 32 maroon balloons, 24 white
balloons, and 16 orange balloons. She wants each arrangement to have the same number of each
color. What is the greatest number of arrangements that she can make if every balloon is used?

• 6

• 2

• 4

• 8

Answer explanation

To find the greatest number of identical arrangements, we need the greatest common divisor (GCD) of 32, 24, and 16. The GCD is 8. Each arrangement can have 4 of each color (32/8, 24/8, 16/8), allowing for 4 total arrangements.