GCF and LCM WORD PROBLEMS - Free Printable
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Step-by-step solution for: GCF and LCM WORD PROBLEMS
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Show Answer Key & Explanations
Step-by-step solution for: GCF and LCM WORD PROBLEMS
Let's solve each of these GCF (Greatest Common Factor) and LCM (Least Common Multiple) word problems step by step. I'll explain the strategy for each, then provide the answer with units.
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- Materials: 20 flyers and 16 buttons
- She wants to distribute them equally to classrooms with no leftovers.
- Each classroom gets an identical set.
- We want the greatest number of classrooms possible.
✔ This is a GCF problem because we're dividing both quantities into equal groups with no remainder.
Find 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 → GCF = 4
So, she can make 4 classrooms, each getting:
- 20 ÷ 4 = 5 flyers
- 16 ÷ 4 = 4 buttons
✔ Answer: 4 classrooms
> Box: GCF
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- 6 granola bars and 10 pieces of dried fruit
- Want identical bags, no leftovers
- Max number of identical bags?
✔ Again, GCF – we’re splitting two items equally.
GCF of 6 and 10:
- Factors of 6: 1, 2, 3, 6
- Factors of 10: 1, 2, 5, 10
- Common: 1, 2 → GCF = 2
Each bag gets:
- 6 ÷ 2 = 3 granola bars
- 10 ÷ 2 = 5 pieces of fruit
✔ Answer: 2 snack bags
> Box: GCF
---
- Both today
- When will he do both again?
✔ This is LCM – find when two events coincide.
LCM of 12 and 6:
- Multiples of 12: 12, 24, 36, ...
- Multiples of 6: 6, 12, 18, 24, ...
- First common multiple: 12
So, he’ll do both again in 12 days
✔ Answer: 12 days
> Box: LCM
---
- 12 bottles of water, 16 cans of food
- Distribute equally among kits
- Max number of kits?
✔ GCF – divide evenly
GCF of 12 and 16:
- 12: 1, 2, 3, 4, 6, 12
- 16: 1, 2, 4, 8, 16
- Common: 1, 2, 4 → GCF = 4
Each kit gets:
- 12 ÷ 4 = 3 bottles
- 16 ÷ 4 = 4 cans
✔ Answer: 4 kits
> Box: GCF
---
- Apple slices in groups of 18
- Grapes in groups of 9
- Wants equal numbers of each
- What’s the smallest number of grapes?
Wait — this says: *"the smallest number of grapes that she can pack"*, but she must have equal numbers of apple slices and grapes.
So, let’s say she packs $ x $ apples and $ x $ grapes.
But apples come in groups of 18 → $ x $ must be a multiple of 18
Grapes come in groups of 9 → $ x $ must be a multiple of 9
We need the smallest number $ x $ that is a multiple of both 18 and 9
✔ This is LCM of 18 and 9
- Multiples of 18: 18, 36, ...
- Multiples of 9: 9, 18, 27, ...
- LCM = 18
So, she can pack 18 grapes (and 18 apple slices)
✔ Answer: 18 grapes
> Box: LCM
---
- Break into groups with same ratio of girls to boys
- No one left out
- Max number of groups?
We want to divide 16 girls and 8 boys into groups where each group has the same combination.
So, we’re looking for the greatest number of groups such that each group has same # of girls and boys.
This means we want to divide both 16 and 8 into equal parts → use GCF
GCF of 16 and 8:
- 16: 1, 2, 4, 8, 16
- 8: 1, 2, 4, 8
- GCF = 8
So, 8 groups:
- 16 ÷ 8 = 2 girls per group
- 8 ÷ 8 = 1 boy per group
✔ Answer: 8 groups
> Box: GCF
---
- 7 roses and 14 daisies
- Arrangements must be identical, no flowers left over
- Greatest number of arrangements?
✔ GCF – split evenly
GCF of 7 and 14:
- 7: 1, 7
- 14: 1, 2, 7, 14
- GCF = 7
Each arrangement gets:
- 7 ÷ 7 = 1 rose
- 14 ÷ 7 = 2 daisies
✔ Answer: 7 arrangements
> Box: GCF
---
- What is the smallest possible number?
✔ This is LCM of 17 and 8
- 17 is prime
- 8 = 2³
- No common factors → LCM = 17 × 8 = 136
✔ Answer: 136
> Box: LCM
---
## ✔ Final Answers:
| Problem | Answer | Strategy |
|--------|--------|---------|
| 1 | 4 classrooms | GCF |
| 2 | 2 snack bags | GCF |
| 3 | 12 days | LCM |
| 4 | 4 kits | GCF |
| 5 | 18 grapes | LCM |
| 6 | 8 groups | GCF |
| 7 | 7 arrangements | GCF |
| 8 | 136 | LCM |
---
Write your answers on the sheet with:
- The number of the question
- The answer including unit (e.g., "4 classrooms", "12 days")
- In the box, write GCF or LCM
Let me know if you'd like this formatted as a printable answer sheet!
---
1. Joanne is campaigning...
- Materials: 20 flyers and 16 buttons
- She wants to distribute them equally to classrooms with no leftovers.
- Each classroom gets an identical set.
- We want the greatest number of classrooms possible.
✔ This is a GCF problem because we're dividing both quantities into equal groups with no remainder.
Find 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 → GCF = 4
So, she can make 4 classrooms, each getting:
- 20 ÷ 4 = 5 flyers
- 16 ÷ 4 = 4 buttons
✔ Answer: 4 classrooms
> Box: GCF
---
2. Serena wants to create snack bags...
- 6 granola bars and 10 pieces of dried fruit
- Want identical bags, no leftovers
- Max number of identical bags?
✔ Again, GCF – we’re splitting two items equally.
GCF of 6 and 10:
- Factors of 6: 1, 2, 3, 6
- Factors of 10: 1, 2, 5, 10
- Common: 1, 2 → GCF = 2
Each bag gets:
- 6 ÷ 2 = 3 granola bars
- 10 ÷ 2 = 5 pieces of fruit
✔ Answer: 2 snack bags
> Box: GCF
---
3. Matthew goes hiking every 12 days and swimming every 6 days...
- Both today
- When will he do both again?
✔ This is LCM – find when two events coincide.
LCM of 12 and 6:
- Multiples of 12: 12, 24, 36, ...
- Multiples of 6: 6, 12, 18, 24, ...
- First common multiple: 12
So, he’ll do both again in 12 days
✔ Answer: 12 days
> Box: LCM
---
4. Mandy is making emergency kits...
- 12 bottles of water, 16 cans of food
- Distribute equally among kits
- Max number of kits?
✔ GCF – divide evenly
GCF of 12 and 16:
- 12: 1, 2, 3, 4, 6, 12
- 16: 1, 2, 4, 8, 16
- Common: 1, 2, 4 → GCF = 4
Each kit gets:
- 12 ÷ 4 = 3 bottles
- 16 ÷ 4 = 4 cans
✔ Answer: 4 kits
> Box: GCF
---
5. Edeena is packing apple slices and grapes...
- Apple slices in groups of 18
- Grapes in groups of 9
- Wants equal numbers of each
- What’s the smallest number of grapes?
Wait — this says: *"the smallest number of grapes that she can pack"*, but she must have equal numbers of apple slices and grapes.
So, let’s say she packs $ x $ apples and $ x $ grapes.
But apples come in groups of 18 → $ x $ must be a multiple of 18
Grapes come in groups of 9 → $ x $ must be a multiple of 9
We need the smallest number $ x $ that is a multiple of both 18 and 9
✔ This is LCM of 18 and 9
- Multiples of 18: 18, 36, ...
- Multiples of 9: 9, 18, 27, ...
- LCM = 18
So, she can pack 18 grapes (and 18 apple slices)
✔ Answer: 18 grapes
> Box: LCM
---
6. A club has 16 girls and 8 boys...
- Break into groups with same ratio of girls to boys
- No one left out
- Max number of groups?
We want to divide 16 girls and 8 boys into groups where each group has the same combination.
So, we’re looking for the greatest number of groups such that each group has same # of girls and boys.
This means we want to divide both 16 and 8 into equal parts → use GCF
GCF of 16 and 8:
- 16: 1, 2, 4, 8, 16
- 8: 1, 2, 4, 8
- GCF = 8
So, 8 groups:
- 16 ÷ 8 = 2 girls per group
- 8 ÷ 8 = 1 boy per group
✔ Answer: 8 groups
> Box: GCF
---
7. Ariel is making flower arrangements...
- 7 roses and 14 daisies
- Arrangements must be identical, no flowers left over
- Greatest number of arrangements?
✔ GCF – split evenly
GCF of 7 and 14:
- 7: 1, 7
- 14: 1, 2, 7, 14
- GCF = 7
Each arrangement gets:
- 7 ÷ 7 = 1 rose
- 14 ÷ 7 = 2 daisies
✔ Answer: 7 arrangements
> Box: GCF
---
8. Wilma is thinking of a number divisible by both 17 and 8...
- What is the smallest possible number?
✔ This is LCM of 17 and 8
- 17 is prime
- 8 = 2³
- No common factors → LCM = 17 × 8 = 136
✔ Answer: 136
> Box: LCM
---
## ✔ Final Answers:
| Problem | Answer | Strategy |
|--------|--------|---------|
| 1 | 4 classrooms | GCF |
| 2 | 2 snack bags | GCF |
| 3 | 12 days | LCM |
| 4 | 4 kits | GCF |
| 5 | 18 grapes | LCM |
| 6 | 8 groups | GCF |
| 7 | 7 arrangements | GCF |
| 8 | 136 | LCM |
---
✍️ Instructions for Student:
Write your answers on the sheet with:
- The number of the question
- The answer including unit (e.g., "4 classrooms", "12 days")
- In the box, write GCF or LCM
Let me know if you'd like this formatted as a printable answer sheet!
Parent Tip: Review the logic above to help your child master the concept of lcm word problems worksheet.
