Math worksheet for finding the least common multiple (LCM) of number pairs.

Let's solve the problem of finding the Least Common Multiple (LCM) for each pair of numbers listed in your worksheet.

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🔍 What is LCM?

The Least Common Multiple (LCM) of two numbers is the smallest positive integer that is divisible by both numbers.

To find the LCM:
1. Prime factorize both numbers.
2. Take the highest power of each prime that appears.
3. Multiply those together.

Alternatively, you can use the formula:
\[
\text{LCM}(a, b) = \frac{a \times b}{\text{GCD}(a, b)}
\]
where GCD is the Greatest Common Divisor.

We'll go through each pair one by one.

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✔ Step-by-step Solutions:

#### 1. 55, 22
- Prime factors:
- 55 = 5 × 11
- 22 = 2 × 11
- LCM = 2 × 5 × 11 = 110

#### 2. 36, 16
- 36 = 2² × 3²
- 16 = 2⁴
- LCM = 2⁴ × 3² = 16 × 9 = 144

#### 3. 8, 30
- 8 = 2³
- 30 = 2 × 3 × 5
- LCM = 2³ × 3 × 5 = 8 × 3 × 5 = 120

#### 4. 108, 3
- 108 = 2² × 3³
- 3 = 3¹
- LCM = 2² × 3³ = 4 × 27 = 108

#### 5. 36, 8
- 36 = 2² × 3²
- 8 = 2³
- LCM = 2³ × 3² = 8 × 9 = 72

#### 6. 5, 15
- 5 = 5
- 15 = 3 × 5
- LCM = 3 × 5 = 15

#### 7. 6, 16
- 6 = 2 × 3
- 16 = 2⁴
- LCM = 2⁴ × 3 = 16 × 3 = 48

#### 8. 11, 88
- 11 = 11
- 88 = 8 × 11 = 2³ × 11
- LCM = 2³ × 11 = 88

#### 9. 2, 32
- 2 = 2
- 32 = 2⁵
- LCM = 2⁵ = 32

#### 10. 11, 5
- 11 and 5 are both prime → LCM = 11 × 5 = 55

#### 11. 9, 63
- 9 = 3²
- 63 = 7 × 9 = 7 × 3²
- LCM = 3² × 7 = 9 × 7 = 63

#### 12. 8, 20
- 8 = 2³
- 20 = 2² × 5
- LCM = 2³ × 5 = 8 × 5 = 40

#### 13. 18, 12
- 18 = 2 × 3²
- 12 = 2² × 3
- LCM = 2² × 3² = 4 × 9 = 36

#### 14. 9, 16
- 9 = 3²
- 16 = 2⁴
- No common factors → LCM = 9 × 16 = 144

#### 15. 15, 21
- 15 = 3 × 5
- 21 = 3 × 7
- LCM = 3 × 5 × 7 = 105

#### 16. 9, 27
- 9 = 3²
- 27 = 3³
- LCM = 3³ = 27

#### 17. 32, 8
- 32 = 2⁵
- 8 = 2³
- LCM = 2⁵ = 32

#### 18. 6, 9
- 6 = 2 × 3
- 9 = 3²
- LCM = 2 × 3² = 2 × 9 = 18

#### 19. 11, 7
- Both prime → LCM = 11 × 7 = 77

#### 20. 16, 14
- 16 = 2⁴
- 14 = 2 × 7
- LCM = 2⁴ × 7 = 16 × 7 = 112

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✔ Final Answers (in order):

| Pair | LCM |
|------------|-------|
| 55, 22 | 110 |
| 36, 16 | 144 |
| 8, 30 | 120 |
| 108, 3 | 108 |
| 36, 8 | 72 |
| 5, 15 | 15 |
| 6, 16 | 48 |
| 11, 88 | 88 |
| 2, 32 | 32 |
| 11, 5 | 55 |
| 9, 63 | 63 |
| 8, 20 | 40 |
| 18, 12 | 36 |
| 9, 16 | 144 |
| 15, 21 | 105 |
| 9, 27 | 27 |
| 32, 8 | 32 |
| 6, 9 | 18 |
| 11, 7 | 77 |
| 16, 14 | 112 |

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📝 Tips:

- Always look for common factors to simplify using the GCD method.
- If one number divides the other, the larger number is the LCM.
- For coprime numbers (no common factors), LCM = product.

Let me know if you'd like a printable version or explanations for any specific pair!