GCF and LCM Word Problems | PDF | Foods | Leisure - Free Printable

Problem Analysis and Solutions

The worksheet involves solving word problems using the concepts of Greatest Common Factor (GCF) and Least Common Multiple (LCM). Let's solve each problem step by step.

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#### Problem 1:
Joanne is campaigning for class president and plans to distribute some campaign materials: 20 flyers and 16 buttons. She wants each classroom to receive an identical set of campaign materials, without having any materials left over. What is the greatest number of classrooms Joanne can distribute materials to?

- Concept: GCF
- Reasoning: To find the greatest number of classrooms that can receive identical sets of materials without leftovers, we need to determine the GCF of 20 and 16.
- Solution:
- Factors of 20: \(1, 2, 4, 5, 10, 20\)
- Factors of 16: \(1, 2, 4, 8, 16\)
- Common factors: \(1, 2, 4\)
- Greatest Common Factor: \(4\)
- Answer: The greatest number of classrooms Joanne can distribute materials to is \(\boxed{4}\).

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#### Problem 2:
Serena wants to create snack bags for a trip she is going on. She has 6 granola bars and 10 pieces of dried fruit. If the snack bags should be identical without any food left over, what is the greatest number of snack bags Serena can make?

- Concept: GCF
- Reasoning: To find the greatest number of identical snack bags, we need to determine the GCF of 6 and 10.
- Solution:
- Factors of 6: \(1, 2, 3, 6\)
- Factors of 10: \(1, 2, 5, 10\)
- Common factors: \(1, 2\)
- Greatest Common Factor: \(2\)
- Answer: The greatest number of snack bags Serena can make is \(\boxed{2}\).

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#### Problem 3:
Matthew goes hiking every 12 days and swimming every 6 days. He did both kinds of exercise today. How many days from now will he go both hiking and swimming again?

- Concept: LCM
- Reasoning: To find when Matthew will next do both activities on the same day, we need to determine the LCM of 12 and 6.
- Solution:
- Prime factorization of 12: \(2^2 \times 3\)
- Prime factorization of 6: \(2 \times 3\)
- LCM: Take the highest power of each prime factor: \(2^2 \times 3 = 12\)
- Answer: Matthew will go both hiking and swimming again in \(\boxed{12}\) days.

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#### Problem 4:
Mandy is making emergency-preparedness kits to share with friends. She has 12 bottles of water and 16 cans of food, which she would like to distribute equally among the kits, with nothing left over. What is the greatest number of kits Mandy can make?

- Concept: GCF
- Reasoning: To find the greatest number of kits Mandy can make, we need to determine the GCF of 12 and 16.
- Solution:
- Factors of 12: \(1, 2, 3, 4, 6, 12\)
- Factors of 16: \(1, 2, 4, 8, 16\)
- Common factors: \(1, 2, 4\)
- Greatest Common Factor: \(4\)
- Answer: The greatest number of kits Mandy can make is \(\boxed{4}\).

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#### Problem 5:
Edeena is packing equal numbers of apple slices and grapes for snacks. Edeena bags the apple slices in groups of 18 and the grapes in groups of 9. What is the smallest number of grapes that she can pack?

- Concept: LCM
- Reasoning: To find the smallest number of grapes that can be packed in groups of 9 while matching the number of apple slices packed in groups of 18, we need to determine the LCM of 18 and 9.
- Solution:
- Prime factorization of 18: \(2 \times 3^2\)
- Prime factorization of 9: \(3^2\)
- LCM: Take the highest power of each prime factor: \(2 \times 3^2 = 18\)
- Answer: The smallest number of grapes that Edeena can pack is \(\boxed{18}\).

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#### Problem 6:
A club has 16 girls and 8 boys as members. The president wants to break the club into groups, with each group containing the same combination of girls and boys. The president also wants to make sure that no one is left out. What is the greatest number of groups the president can make?

- Concept: GCF
- Reasoning: To find the greatest number of groups that can be formed with the same combination of girls and boys, we need to determine the GCF of 16 and 8.
- Solution:
- Factors of 16: \(1, 2, 4, 8, 16\)
- Factors of 8: \(1, 2, 4, 8\)
- Common factors: \(1, 2, 4, 8\)
- Greatest Common Factor: \(8\)
- Answer: The greatest number of groups the president can make is \(\boxed{8}\).

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#### Problem 7:
Ariel is making flower arrangements. He has 7 roses and 14 daisies. If Ariel wants to make all the arrangements identical and have no flowers left over, what is the greatest number of flower arrangements that he can make?

- Concept: GCF
- Reasoning: To find the greatest number of identical flower arrangements, we need to determine the GCF of 7 and 14.
- Solution:
- Factors of 7: \(1, 7\)
- Factors of 14: \(1, 2, 7, 14\)
- Common factors: \(1, 7\)
- Greatest Common Factor: \(7\)
- Answer: The greatest number of flower arrangements Ariel can make is \(\boxed{7}\).

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#### Problem 8:
Wilma is thinking of a number that is divisible by both 17 and 8. What is the smallest possible number that Wilma could be thinking of?

- Concept: LCM
- Reasoning: To find the smallest number divisible by both 17 and 8, we need to determine the LCM of 17 and 8.
- Solution:
- Prime factorization of 17: \(17\) (prime number)
- Prime factorization of 8: \(2^3\)
- LCM: Take the highest power of each prime factor: \(2^3 \times 17 = 136\)
- Answer: The smallest possible number Wilma could be thinking of is \(\boxed{136}\).

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Final Answers:

1. \(\boxed{4}\)
2. \(\boxed{2}\)
3. \(\boxed{12}\)
4. \(\boxed{4}\)
5. \(\boxed{18}\)
6. \(\boxed{8}\)
7. \(\boxed{7}\)
8. \(\boxed{136}\)