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

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

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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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1. 16, 10

- Prime factors:
- 16 = $2^4$
- 10 = $2 \times 5$
- GCF: common factor = $2$ → GCF = 2
- LCM: take highest powers: $2^4 \times 5 = 16 \times 5 = 80$ → LCM = 80

✔ LCM = 80, GCF = 2

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2. 14, 6

- Prime factors:
- 14 = $2 \times 7$
- 6 = $2 \times 3$
- GCF: common factor = $2$ → GCF = 2
- LCM: $2 \times 3 \times 7 = 42$ → LCM = 42

✔ LCM = 42, GCF = 2

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3. 3, 27

- Prime factors:
- 3 = $3$
- 27 = $3^3$
- GCF: $3$ → GCF = 3
- LCM: $3^3 = 27$ → LCM = 27

✔ LCM = 27, GCF = 3

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4. 6, 14

- Prime factors:
- 6 = $2 \times 3$
- 14 = $2 \times 7$
- GCF: $2$ → GCF = 2
- LCM: $2 \times 3 \times 7 = 42$ → LCM = 42

✔ LCM = 42, GCF = 2

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5. 16, 5

- Prime factors:
- 16 = $2^4$
- 5 = $5$
- GCF: no common factors → GCF = 1
- LCM: $2^4 \times 5 = 16 \times 5 = 80$ → LCM = 80

✔ LCM = 80, GCF = 1

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6. 8, 12

- Prime factors:
- 8 = $2^3$
- 12 = $2^2 \times 3$
- GCF: $2^2 = 4$ → GCF = 4
- LCM: $2^3 \times 3 = 8 \times 3 = 24$ → LCM = 24

✔ LCM = 24, GCF = 4

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7. 16, 6

- Prime factors:
- 16 = $2^4$
- 6 = $2 \times 3$
- GCF: $2$ → GCF = 2
- LCM: $2^4 \times 3 = 16 \times 3 = 48$ → LCM = 48

✔ LCM = 48, GCF = 2

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8. 8, 3

- Prime factors:
- 8 = $2^3$
- 3 = $3$
- GCF: no common factors → GCF = 1
- LCM: $2^3 \times 3 = 8 \times 3 = 24$ → LCM = 24

✔ LCM = 24, GCF = 1

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✔ Final Answer Table:

| 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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