LCM and GCF Worksheets (printable, online, answers, examples) - Free Printable

Let's solve each pair of numbers for their Least Common Multiple (LCM) and Greatest Common Factor (GCF) step by step.

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🔹 Definitions:

- GCF (Greatest Common Factor): The largest number that divides both numbers evenly.
- LCM (Least Common Multiple): The smallest number that is a multiple of both numbers.

We'll use prime factorization or listing methods where appropriate.

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✔ Problem 1: 16, 10

- Prime factors:
- 16 = 2⁴
- 10 = 2 × 5
- GCF: Common prime factor → 2¹ → 2
- LCM: Take highest powers → 2⁴ × 5 = 16 × 5 = 80

✔ LCM = 80, GCF = 2

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✔ Problem 2: 14, 6

- Prime factors:
- 14 = 2 × 7
- 6 = 2 × 3
- GCF: Common factor → 2 → 2
- LCM: 2 × 3 × 7 = 42

✔ LCM = 42, GCF = 2

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✔ Problem 3: 3, 27

- Prime factors:
- 3 = 3
- 27 = 3³
- GCF: 3¹ → 3
- LCM: 3³ = 27

✔ LCM = 27, GCF = 3

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✔ Problem 4: 6, 14

- Prime factors:
- 6 = 2 × 3
- 14 = 2 × 7
- GCF: 2 → 2
- LCM: 2 × 3 × 7 = 42

✔ LCM = 42, GCF = 2

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✔ Problem 5: 16, 5

- Prime factors:
- 16 = 2⁴
- 5 = 5
- GCF: No common factors → 1
- LCM: 2⁴ × 5 = 16 × 5 = 80

✔ LCM = 80, GCF = 1

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✔ Problem 6: 8, 12

- Prime factors:
- 8 = 2³
- 12 = 2² × 3
- GCF: 2² = 4
- LCM: 2³ × 3 = 8 × 3 = 24

✔ LCM = 24, GCF = 4

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✔ Problem 7: 16, 6

- Prime factors:
- 16 = 2⁴
- 6 = 2 × 3
- GCF: 2 → 2
- LCM: 2⁴ × 3 = 16 × 3 = 48

✔ LCM = 48, GCF = 2

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✔ Problem 8: 8, 3

- Prime factors:
- 8 = 2³
- 3 = 3
- GCF: No common factors → 1
- LCM: 2³ × 3 = 8 × 3 = 24

✔ LCM = 24, GCF = 1

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📝 Final Answers:

| Numbers | LCM | GCF |
|--------|------|-----|
| 16, 10 | 80 | 2 |
| 14, 6 | 42 | 2 |
| 3, 27 | 27 | 3 |
| 6, 14 | 42 | 2 |
| 16, 5 | 80 | 1 |
| 8, 12 | 24 | 4 |
| 16, 6 | 48 | 2 |
| 8, 3 | 24 | 1 |

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✔ Answer Key:

```
LCM GCF
80 2
42 2
27 3
42 2
80 1
24 4
48 2
24 1
```

Let me know if you'd like a printable version or explanations using lists instead of prime factorization!