GCF and LCM

There are 14 girls and 21 boys in Mrs. Andrew's gym class. To play a certain game, the students must form teams. Each team must have the same number of boys and girls. What is the greatest number of teams Mrs. Andrews can make if every student is on a team?

• 7 teams
• 14 teams
• 21 teams
• 42 teams

As 100 students entered the auditorium some were given a prize.  If every 6th student received a pencil and every 9th student received a notebook. How many participants received both a pencil and a notebook?

• 3 students
• 18 students
• 5 students
• 54 students

Ralph and his brother are at the state fair. They separate from each other at the ferris wheel at 1:00 PM, and they agree that they will meet back at the ferris wheel from time to time to see whether each other is ready to leave. Ralph checks the ferris wheel every 15 minutes, and Joe checks the ferris wheel every 24 minutes. At what time will they meet at the ferris wheel again?

• 120 Minutes
• 3 Minutes
• 1:20PM
• 3:00 PM

Mrs. McCoy makes flower arrangements. She has 36 red carnations, 60 white carnations, and 72 pink carnations. Each arrangement must have the same number of each color. What is the greatest number of arrangements she can make if she uses every carnation?

• 12 flowers
• 12 arrangements
• 1,080 arrangements
• 6 arrangements 

Juice comes in packs of 6 and granola bars come in packs of 8. If there are 24 players on the soccer team, what is the least number of packs needed so that each player has a drink and granola bar, and there are none left over?

• 3 packs juice, 4 packs granola bars
• 12 packs of both
• 4 packs juice, 3 packs granola bars

Vince has 12 jars of grape jam, 16 jars of strawberry jam, and 24 jars of raspberry jam. he wants to place the jam into the greatest number of boxes possible so that each box has the same number of jars of each kind of jam. How many boxes does he need?

• 4 boxes
• 3 boxes
• 6 boxes
• 12 boxes

Carolyn has 24 bottles of shampoo, 36 tubes of hand lotion, and 60 bars of lavender soap to make gift baskets. She wants to have the same number of each item in every basket. What is the greatest number of baskets she can make without having any of the items left over?

• 4 baskets
• 60 baskets
• 6 baskets
• 12 baskets

Two faucets are dripping. One faucet drips every 4 seconds and the other faucet drips every 9 seconds. If a drop of water falls from both faucets at the same time, how many seconds will it be before you see the faucets drip at the same time?

• 18 seconds
• 36 seconds
• 72 seconds
• 1 second

Mr. Stevenson is ordering shirts and hats for his Boy Scout Troop. There are 60 scouts in the troop. Hats come in packs of 3, and shirts come in packs of 5. What is the least number of packs each he should order so that each scout has 1 hat and 1 shirt, and none are left over?

• 32 packs
• 12 hat packs, 20 shirt packs
• 10 hat packs, 24 shirt packs
• 20 hat packs, 12 shirt packs

Mr. Thompson's class was competing in field day. There were 16 students wearing blue shirts and 12 students wearing red shirts. He divided the class into the greatest number of teams possible with the same number of of blue and red shirts on each team. How many students with each color shirt are on each team?

• 3 red, 4 blue
• 4 red, 3 blue
• 4 teams
• 48 teams