GCF and LCM Word Problems

What does the question below require you to find? A string of holiday lights at a store have three colors that flash at different times. Red lights flash every fifth second. Blue lights flash every third seconds. Green light flashes every four seconds. The store owner turns on the lights. After how many seconds will all three lights flash at the same time for the first time?

• Greatest Common Factor

• Least Common Multiple

What does the question below require you to find? Elena has 20 apples and 35 crackers for making snack bags. She wants to make as many snack bags as possible and wants each bag to have the same combination of apples and crackers. What is the largest number of snack bags she could make?

• Greatest Common Factor

• Least Common Multiple

A veterinarian has 36 dog biscuits and 45 Denta Stix for the dogs in her neighborhood. She wants to make gift bags for her clients. What is the greatest number of gift bags that she can make and have no left over biscuits or Denta Stix?

• 3 gift bags

• 6 gift bags

• 9 gift bags

• 15 gift bags

Train A makes its stops in 45 minutes. Train B makes its stops in 60 minutes. How many minutes will pass before the two trains meet? In this time, how many loops will Train A make? How many loops will Train B make?

• The trains will meet in 15 minutes. Train A will make 3 loops and Train B will make 4 loops.

• The trains will meet in 180 minutes. Train A will make 4 loops and Train B will make 3 loops.

• The trains will meet in 190 minutes. Train A will make 2 loops and Train B will make 1 loops.

• The trains will meet in 120 minutes. Train A will make 3 loops and Train B will make 2 loops.

The school nurse is assembling first-aid kits for the teachers. She has 75 bandages and 90 cough drops. All the kits must have the same number of each supply, and all supplies must be used. What is the largest number of kits the nurse can make?

• The nurse can make 5 kits.

• The nurse can make 8 kits.

• The nurse can make 10 kits.

• The nurse can make 15 kits.

Madison found the paper plates and matching cups that she wants to use for her party. The plates are packaged 8 to a pack. The cups are packaged 10 to a pack. What is the smallest number of plates and cups Madison needs to but so that she has the same amount of each? How many packages of each does Madison need to buy?

• Madison will need 18 plates and 18 cups. She will need to buy 2 packs of plates and 2 packs of cups.

• Madison will need 80 plates and 80 cups. She will need to buy 10 packs of plates and 8 packs of cups.

• Madison will need 2 packages of each.

• Madison will need 40 plates and 40 cups. She will need to buy 5 packs of plates and 4 packs of cups.