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

Sure! Let’s solve each pair for LCM (Least Common Multiple) and GCF (Greatest Common Factor). I’ll explain the method as we go.

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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.

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## ✔ 1. 16, 10

Prime factorization:
- 16 = 2 × 2 × 2 × 2 = 2⁴
- 10 = 2 × 5

GCF: Take common primes with lowest exponent → only 2¹ → GCF = 2

LCM: Take all primes with highest exponent → 2⁴ × 5 = 16 × 5 = 80

✔ LCM = 80, GCF = 2

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## ✔ 2. 14, 6

Prime factorization:
- 14 = 2 × 7
- 6 = 2 × 3

GCF: Common prime → 2

LCM: 2 × 3 × 7 = 42

✔ LCM = 42, GCF = 2

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## ✔ 3. 3, 27

Prime factorization:
- 3 = 3
- 27 = 3 × 3 × 3 = 3³

GCF: Common prime → 3¹ → GCF = 3

LCM: Highest power → 3³ = 27

✔ LCM = 27, GCF = 3

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## ✔ 4. 6, 14

Same as #2 — just reversed.

Prime factorization:
- 6 = 2 × 3
- 14 = 2 × 7

GCF: 2

LCM: 2 × 3 × 7 = 42

✔ LCM = 42, GCF = 2

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## ✔ 5. 16, 5

Prime factorization:
- 16 = 2⁴
- 5 = 5

No common primes → GCF = 1

LCM: 2⁴ × 5 = 16 × 5 = 80

✔ LCM = 80, GCF = 1

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## ✔ 6. 8, 12

Prime factorization:
- 8 = 2³
- 12 = 2² × 3

GCF: Common prime → 2² = 4

LCM: 2³ × 3 = 8 × 3 = 24

✔ LCM = 24, GCF = 4

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## ✔ 7. 16, 6

Prime factorization:
- 16 = 2⁴
- 6 = 2 × 3

GCF: 2¹ = 2

LCM: 2⁴ × 3 = 16 × 3 = 48

✔ LCM = 48, GCF = 2

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## ✔ 8. 8, 3

Prime factorization:
- 8 = 2³
- 3 = 3

No common primes → GCF = 1

LCM: 2³ × 3 = 8 × 3 = 24

✔ LCM = 24, GCF = 1

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## 📝 Final Answers:

| Pair | 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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✔ You can now fill in the worksheet with these answers!

Let me know if you’d like to see how to solve using listing multiples or Euclidean algorithm for GCF!