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

Sure! Let’s solve each problem step by step. The Least Common Multiple (LCM) of two numbers is the smallest positive number that is a multiple of both.

There are several methods to find LCM:
- Listing multiples (good for small numbers)
- Prime factorization (most reliable)
- Using the formula:
`LCM(a, b) = (a × b) / GCF(a, b)`
(GCF = Greatest Common Factor)

I’ll use prime factorization and/or the formula for accuracy.

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1) LCM(8, 12)

Prime factors:
- 8 = 2³
- 12 = 2² × 3

Take highest power of each prime:
→ 2³ × 3 = 8 × 3 = 24

✔ Answer: 24

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2) LCM(20, 40)

Note: 40 is a multiple of 20 → so LCM is 40

Check with formula:
GCF(20, 40) = 20
LCM = (20 × 40) / 20 = 40

✔ Answer: 40

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3) LCM(22, 6)

Prime factors:
- 22 = 2 × 11
- 6 = 2 × 3

LCM = 2 × 3 × 11 = 66

✔ Answer: 66

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4) LCM(14, 4)

Prime factors:
- 14 = 2 × 7
- 4 = 2²

LCM = 2² × 7 = 4 × 7 = 28

✔ Answer: 28

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5) LCM(42, 30)

Prime factors:
- 42 = 2 × 3 × 7
- 30 = 2 × 3 × 5

LCM = 2 × 3 × 5 × 7 = 210

✔ Answer: 210

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6) LCM(24, 32)

Prime factors:
- 24 = 2³ × 3
- 32 = 2⁵

LCM = 2⁵ × 3 = 32 × 3 = 96

✔ Answer: 96

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7) LCM(15, 9)

Prime factors:
- 15 = 3 × 5
- 9 = 3²

LCM = 3² × 5 = 9 × 5 = 45

✔ Answer: 45

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8) LCM(45, 27)

Prime factors:
- 45 = 3² × 5
- 27 = 3³

LCM = 3³ × 5 = 27 × 5 = 135

✔ Answer: 135

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9) LCM(34, 26)

Prime factors:
- 34 = 2 × 17
- 26 = 2 × 13

LCM = 2 × 13 × 17 = 26 × 17 = 442

✔ Answer: 442

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10) LCM(10, 48)

Prime factors:
- 10 = 2 × 5
- 48 = 2⁴ × 3

LCM = 2⁴ × 3 × 5 = 16 × 3 × 5 = 48 × 5 = 240

✔ Answer: 240

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## ✔ Final Answers:

1) 24
2) 40
3) 66
4) 28
5) 210
6) 96
7) 45
8) 135
9) 442
10) 240

Let me know if you’d like to see the step-by-step using another method (like listing multiples or GCF formula) for any of them!