GCF and LCM - Free Printable

You're asked to find the GCF (Greatest Common Factor) and LCM (Least Common Multiple) for each pair of numbers.

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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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✔ Useful Formula:

For any two numbers `a` and `b`:
> GCF(a, b) × LCM(a, b) = a × b

So if you find one, you can find the other using this formula.

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Let’s solve each problem step by step.

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## 1) 40, 25

Prime factorization:
- 40 = 2³ × 5
- 25 = 5²

→ GCF = common prime factors with lowest powers = 5

→ LCM = all prime factors with highest powers = 2³ × 5² = 8 × 25 = 200

✔ GCF = 5, LCM = 200

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## 2) 24, 40

Prime factorization:
- 24 = 2³ × 3
- 40 = 2³ × 5

→ GCF = 2³ = 8

→ LCM = 2³ × 3 × 5 = 8 × 15 = 120

✔ GCF = 8, LCM = 120

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## 3) 7, 15

Both are prime or coprime (no common factors except 1).

→ GCF = 1

→ LCM = 7 × 15 = 105

✔ GCF = 1, LCM = 105

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## 4) 32, 16

32 is a multiple of 16.

→ GCF = smaller number = 16

→ LCM = larger number = 32

✔ GCF = 16, LCM = 32

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## 5) 15, 9

Prime factorization:
- 15 = 3 × 5
- 9 = 3²

→ GCF = 3

→ LCM = 3² × 5 = 9 × 5 = 45

✔ GCF = 3, LCM = 45

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## 6) 22, 33

Prime factorization:
- 22 = 2 × 11
- 33 = 3 × 11

→ GCF = 11

→ LCM = 2 × 3 × 11 = 66

✔ GCF = 11, LCM = 66

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## 7) 9, 20

Coprime (no common factors except 1).

→ GCF = 1

→ LCM = 9 × 20 = 180

✔ GCF = 1, LCM = 180

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## 8) 24, 30

Prime factorization:
- 24 = 2³ × 3
- 30 = 2 × 3 × 5

→ GCF = 2 × 3 = 6

→ LCM = 2³ × 3 × 5 = 8 × 3 × 5 = 120

✔ GCF = 6, LCM = 120

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## 9) 11, 15

Both are prime to each other.

→ GCF = 1

→ LCM = 11 × 15 = 165

✔ GCF = 1, LCM = 165

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## 10) 50, 70

Prime factorization:
- 50 = 2 × 5²
- 70 = 2 × 5 × 7

→ GCF = 2 × 5 = 10

→ LCM = 2 × 5² × 7 = 2 × 25 × 7 = 350

✔ GCF = 10, LCM = 350

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## 📋 Final Answers Table:

| # | Numbers | GCF | LCM |
|----|---------|-----|------|
| 1) | 40, 25 | 5 | 200 |
| 2) | 24, 40 | 8 | 120 |
| 3) | 7, 15 | 1 | 105 |
| 4) | 32, 16 | 16 | 32 |
| 5) | 15, 9 | 3 | 45 |
| 6) | 22, 33 | 11 | 66 |
| 7) | 9, 20 | 1 | 180 |
| 8) | 24, 30 | 6 | 120 |
| 9) | 11, 15 | 1 | 165 |
|10) | 50, 70 | 10 | 350 |

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✔ All problems solved! You can now fill in your worksheet with these answers. Let me know if you’d like to see how to use the “listing method” or “Euclidean algorithm” for GCF too!