Worksheet to find GCF and LCM of number pairs.

Sure! Let’s solve each pair of numbers for Greatest Common Factor (GCF) and Least Common Multiple (LCM).

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🔢 Definitions Recap:

- GCF = largest number that divides both numbers evenly.
- LCM = smallest number that is a multiple of both numbers.

We can use prime factorization or the Euclidean algorithm for GCF, and then use the formula:
> LCM(a, b) = (a × b) / GCF(a, b)

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## ✔ Problem 1: 60, 66

Prime factorization:
- 60 = 2² × 3 × 5
- 66 = 2 × 3 × 11

GCF = common primes with lowest powers → 2 × 3 = 6

LCM = all primes with highest powers → 2² × 3 × 5 × 11 = 4 × 3 × 5 × 11 = 660

✔ GCF = 6, LCM = 660

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## ✔ Problem 2: 44, 14

Prime factorization:
- 44 = 2² × 11
- 14 = 2 × 7

GCF = 2

LCM = 2² × 7 × 11 = 4 × 7 × 11 = 308

✔ GCF = 2, LCM = 308

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## ✔ Problem 3: 7, 56

Note: 56 ÷ 7 = 8 → so 7 divides 56 exactly.

GCF = 7 (since 7 is a factor of 56)

LCM = 56 (since 56 is a multiple of 7)

✔ GCF = 7, LCM = 56

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## ✔ Problem 4: 20, 22

Prime factorization:
- 20 = 2² × 5
- 22 = 2 × 11

GCF = 2

LCM = 2² × 5 × 11 = 4 × 5 × 11 = 220

✔ GCF = 2, LCM = 220

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## ✔ Problem 5: 13, 31

Both are prime numbers, and different.

GCF = 1 (no common factors other than 1)

LCM = 13 × 31 = 403

✔ GCF = 1, LCM = 403

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## ✔ Problem 6: 8, 42

Prime factorization:
- 8 = 2³
- 42 = 2 × 3 × 7

GCF = 2

LCM = 2³ × 3 × 7 = 8 × 3 × 7 = 168

✔ GCF = 2, LCM = 168

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## ✔ Problem 7: 16, 60

Prime factorization:
- 16 = 2⁴
- 60 = 2² × 3 × 5

GCF = 2² = 4

LCM = 2⁴ × 3 × 5 = 16 × 3 × 5 = 240

✔ GCF = 4, LCM = 240

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## 📋 Final Answers Table:

| Pair | GCF | LCM |
|----------|-----|------|
| 1. 60, 66 | 6 | 660 |
| 2. 44, 14 | 2 | 308 |
| 3. 7, 56 | 7 | 56 |
| 4. 20, 22 | 2 | 220 |
| 5. 13, 31 | 1 | 403 |
| 6. 8, 42 | 2 | 168 |
| 7. 16, 60 | 4 | 240 |

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

Let me know if you’d like to see step-by-step Euclidean algorithm or visual methods too!