GCF and LCM Word Problems worksheet for math practice.

Let’s go through each problem one by one. We’ll figure out whether to use GCF (Greatest Common Factor) or LCM (Least Common Multiple), then solve it step by step.

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Problem 1:
Joanne has 20 flyers and 16 buttons. She wants to make identical sets with nothing left over. What’s the greatest number of classrooms she can give materials to?

→ This is about dividing both numbers evenly into groups — so we need the GCF of 20 and 16.

Factors of 20: 1, 2, 4, 5, 10, 20
Factors of 16: 1, 2, 4, 8, 16
Common factors: 1, 2, 4 → Greatest is 4

✔ Answer: 4 classrooms

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Problem 2:
Serena has 6 granola bars and 10 pieces of dried fruit. She wants identical snack bags with no food left over. Greatest number of bags?

→ Again, dividing into equal groups → GCF of 6 and 10.

Factors of 6: 1, 2, 3, 6
Factors of 10: 1, 2, 5, 10
Common factors: 1, 2 → Greatest is 2

✔ Answer: 2 snack bags

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Problem 3:
Matthew hikes every 12 days, swims every 6 days. He did both today. When will he do both again?

→ We’re looking for when the two schedules line up again → LCM of 12 and 6.

Multiples of 12: 12, 24, 36...
Multiples of 6: 6, 12, 18, 24...
First common multiple: 12

✔ Answer: 12 days from now

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Problem 4:
Mandy has 12 bottles of water and 16 cans of food. Distribute equally into kits with nothing left over. Greatest number of kits?

→ Dividing into equal groups → GCF of 12 and 16.

Factors of 12: 1, 2, 3, 4, 6, 12
Factors of 16: 1, 2, 4, 8, 16
Common factors: 1, 2, 4 → Greatest is 4

✔ Answer: 4 kits

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Problem 5:
Edeena packs apple slices in groups of 18 and grapes in groups of 9. What’s the smallest number of grapes she can pack if apples and grapes are packed in equal total amounts?

Wait — re-read: “packing equal numbers of apple slices and grapes” — meaning same total count of each? But she packs apples in groups of 18, grapes in groups of 9. So we want the smallest number that is a multiple of both 18 and 9 → LCM

Multiples of 18: 18, 36, 54...
Multiples of 9: 9, 18, 27, 36...
Smallest common multiple: 18

But question asks: “smallest number of grapes that she can pack?” Since grapes come in groups of 9, and we need total grapes = total apples = 18, then grapes = 18.

✔ Answer: 18 grapes

*(Note: If interpreted as “how many grape groups”, it would be 2, but question says “number of grapes”, so 18.)*

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Problem 6:
Club has 16 girls and 8 boys. Break into groups with same combination of girls and boys, no one left out. Greatest number of groups?

→ Same combo per group → divide both numbers evenly → GCF of 16 and 8.

Factors of 16: 1, 2, 4, 8, 16
Factors of 8: 1, 2, 4, 8
Greatest common factor: 8

Check: 16 ÷ 8 = 2 girls per group; 8 ÷ 8 = 1 boy per group → works!

✔ Answer: 8 groups

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Problem 7:
Ariel has 7 roses and 14 daisies. Make identical arrangements with no flowers left over. Greatest number of arrangements?

→ Divide both evenly → GCF of 7 and 14.

Factors of 7: 1, 7
Factors of 14: 1, 2, 7, 14
Greatest common factor: 7

Check: 7 ÷ 7 = 1 rose per arrangement; 14 ÷ 7 = 2 daisies per arrangement → perfect.

✔ Answer: 7 arrangements

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Problem 8:
Wilma is thinking of a number divisible by both 17 and 8. Smallest possible number?

→ Number divisible by both → must be a common multiple → smallest is LCM of 17 and 8.

Since 17 is prime and doesn’t share factors with 8, LCM = 17 × 8 = 136

✔ Answer: 136

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Final Answer:
1. 4
2. 2
3. 12
4. 4
5. 18
6. 8
7. 7
8. 136