Math worksheet for finding least common multiples of number pairs.

Let's solve the Least Common Multiple (LCM) problems step by step.

We are given pairs of numbers and need to find their common multiples and then the least common multiple (LCM). The LCM is the smallest number that is a multiple of both numbers in the pair.

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🔷 How to Find LCM:

There are two main methods:

1. List Multiples Method: List multiples of each number until you find the smallest common one.
2. Prime Factorization Method: Break down each number into prime factors, then take the highest power of each prime and multiply.

We'll use the list method for clarity, especially since the numbers aren't too large.

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Let’s go through each problem:

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1. (15, 20)

- Multiples of 15: 15, 30, 45, 60, 75, 90, 105, 120, ...
- Multiples of 20: 20, 40, 60, 80, 100, 120, ...
- Common multiples: 60, 120, ...
- LCM = 60

✔ Already given: 30 — wait! That’s incorrect.
But in the worksheet, it says LCM = 30, but 30 is not a multiple of 20 → So this is a mistake.

Actually, 30 is a multiple of 15, but not of 20 → so 30 cannot be the LCM.

So correct answer: ✔ LCM = 60

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2. (10, 25)

- Multiples of 10: 10, 20, 30, 40, 50, 60, 70, ...
- Multiples of 25: 25, 50, 75, 100, ...
- Common: 50, 100, ...
- LCM = 50

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3. (8, 12)

- Multiples of 8: 8, 16, 24, 32, 40, 48, ...
- Multiples of 12: 12, 24, 36, 48, ...
- Common: 24, 48, ...
- LCM = 24

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4. (10, 12)

- Multiples of 10: 10, 20, 30, 40, 50, 60, ...
- Multiples of 12: 12, 24, 36, 48, 60, ...
- Common: 60, 120, ...
- LCM = 60

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5. (20, 25)

- Multiples of 20: 20, 40, 60, 80, 100, 120, ...
- Multiples of 25: 25, 50, 75, 100, 125, ...
- Common: 100, 200, ...
- LCM = 100

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6. (10, 20)

- Multiples of 10: 10, 20, 30, 40, ...
- Multiples of 20: 20, 40, 60, ...
- Common: 20, 40, ...
- LCM = 20

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7. (20, 30)

- Multiples of 20: 20, 40, 60, 80, 100, ...
- Multiples of 30: 30, 60, 90, 120, ...
- Common: 60, 120, ...
- LCM = 60

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8. (40, 20)

- Since 40 is a multiple of 20 → LCM = 40
- Multiples of 40: 40, 80, ...
- Multiples of 20: 20, 40, 60, ...
- Common: 40, 80, ...
- LCM = 40

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9. (15, 30)

- 30 is a multiple of 15 → LCM = 30
- Multiples of 15: 15, 30, 45, ...
- Multiples of 30: 30, 60, ...
- Common: 30, 60, ...
- LCM = 30

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10. (6, 18)

- 18 is a multiple of 6 → LCM = 18
- Multiples of 6: 6, 12, 18, 24, ...
- Multiples of 18: 18, 36, ...
- Common: 18, 36, ...
- LCM = 18

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11. (4, 20)

- 20 is a multiple of 4 → LCM = 20
- Multiples of 4: 4, 8, 12, 16, 20, ...
- Multiples of 20: 20, 40, ...
- Common: 20, 40, ...
- LCM = 20

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12. (12, 15)

- Multiples of 12: 12, 24, 36, 48, 60, 72, ...
- Multiples of 15: 15, 30, 45, 60, 75, ...
- Common: 60, 120, ...
- LCM = 60

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13. (7, 42)

- 42 is a multiple of 7 → LCM = 42
- Multiples of 7: 7, 14, 21, 28, 35, 42, ...
- Multiples of 42: 42, 84, ...
- Common: 42, 84, ...
- LCM = 42

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14. (5, 12)

- Multiples of 5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, ...
- Multiples of 12: 12, 24, 36, 48, 60, ...
- Common: 60, 120, ...
- LCM = 60

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15. (18, 24)

- Multiples of 18: 18, 36, 54, 72, 90, ...
- Multiples of 24: 24, 48, 72, 96, ...
- Common: 72, 144, ...
- LCM = 72

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## ✔ Final Answers:

| Problem | Pair | LCM |
|--------|------------|-----|
| 1 | (15, 20) | 60 |
| 2 | (10, 25) | 50 |
| 3 | (8, 12) | 24 |
| 4 | (10, 12) | 60 |
| 5 | (20, 25) | 100 |
| 6 | (10, 20) | 20 |
| 7 | (20, 30) | 60 |
| 8 | (40, 20) | 40 |
| 9 | (15, 30) | 30 |
| 10 | (6, 18) | 18 |
| 11 | (4, 20) | 20 |
| 12 | (12, 15) | 60 |
| 13 | (7, 42) | 42 |
| 14 | (5, 12) | 60 |
| 15 | (18, 24) | 72 |

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🚨 Note:

The worksheet incorrectly lists LCM = 30 for problem 1. But 30 is not divisible by 20, so it cannot be a common multiple. Correct LCM is 60.

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Let me know if you'd like a printable version or explanation using prime factorization!