Grade 6 Math Worksheet - Least common multiple (LCM) (2-50) | Worsheets library... - Free Printable

Let's solve the Least Common Multiple (LCM) problems from the worksheet step by step. The goal is to find the smallest number that is a multiple of both given numbers.

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🔹 How to Find LCM:

There are two main methods:
1. Prime Factorization Method – Break down each number into prime factors, then take the highest power of each prime.
2. Listing Multiples – List multiples of each number until you find the smallest common one.

We’ll use prime factorization for efficiency.

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Let’s go through each problem:

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1. 43 and 22

- 43 is a prime number → 43
- 22 = 2 × 11

No common factors → LCM = 43 × 2 × 11 = 946

✔ Answer: 946

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2. 27 and 35

- 27 = 3³
- 35 = 5 × 7

No common factors → LCM = 3³ × 5 × 7 = 27 × 5 × 7 = 945

✔ Answer: 945

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3. 36 and 8

- 36 = 2² × 3²
- 8 = 2³

Take the highest powers: 2³ × 3² = 8 × 9 = 72

✔ Answer: 72

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4. 40 and 35

- 40 = 2³ × 5
- 35 = 5 × 7

LCM = 2³ × 5 × 7 = 8 × 5 × 7 = 280

✔ Answer: 280

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5. 5 and 17

Both are prime numbers, so LCM = 5 × 17 = 85

✔ Answer: 85

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6. 5 and 41

Both prime → LCM = 5 × 41 = 205

✔ Answer: 205

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7. 9 and 13

- 9 = 3²
- 13 = prime

No common factors → LCM = 3² × 13 = 9 × 13 = 117

✔ Answer: 117

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8. 13 and 9

Same as #7 → 13 × 9 = 117

✔ Answer: 117

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9. 36 and 22

- 36 = 2² × 3²
- 22 = 2 × 11

LCM = 2² × 3² × 11 = 4 × 9 × 11 = 396

✔ Answer: 396

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10. 50 and 12

- 50 = 2 × 5²
- 12 = 2² × 3

LCM = 2² × 3 × 5² = 4 × 3 × 25 = 300

✔ Answer: 300

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11. 50 and 16

- 50 = 2 × 5²
- 16 = 2⁴

LCM = 2⁴ × 5² = 16 × 25 = 400

✔ Answer: 400

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12. 37 and 19

Both are prime numbers → LCM = 37 × 19 = 703

✔ Answer: 703

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13. 8 and 6

- 8 = 2³
- 6 = 2 × 3

LCM = 2³ × 3 = 8 × 3 = 24

✔ Answer: 24

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14. 22 and 9

- 22 = 2 × 11
- 9 = 3²

No common factors → LCM = 2 × 3² × 11 = 2 × 9 × 11 = 198

✔ Answer: 198

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15. 34 and 4

- 34 = 2 × 17
- 4 = 2²

LCM = 2² × 17 = 4 × 17 = 68

✔ Answer: 68

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16. 5 and 8

- 5 = prime
- 8 = 2³

No common factors → LCM = 5 × 8 = 40

✔ Answer: 40

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✔ Final Answers:

| Problem | Numbers | LCM |
|--------|-------------|-------|
| 1 | 43, 22 | 946 |
| 2 | 27, 35 | 945 |
| 3 | 36, 8 | 72 |
| 4 | 40, 35 | 280 |
| 5 | 5, 17 | 85 |
| 6 | 5, 41 | 205 |
| 7 | 9, 13 | 117 |
| 8 | 13, 9 | 117 |
| 9 | 36, 22 | 396 |
| 10 | 50, 12 | 300 |
| 11 | 50, 16 | 400 |
| 12 | 37, 19 | 703 |
| 13 | 8, 6 | 24 |
| 14 | 22, 9 | 198 |
| 15 | 34, 4 | 68 |
| 16 | 5, 8 | 40 |

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