Lowest common multiple (LCM) worksheet for Grade 5 students, featuring 14 problems to find the LCM of number pairs.

Let's solve each problem on the Lowest Common Multiple (LCM) worksheet step by step. The goal is to find the least common multiple of two numbers for each question.

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🔹 What is LCM?

The Least Common Multiple (LCM) of two numbers is the smallest number that is a multiple of both.

We can find the LCM using:
1. Prime factorization method, or
2. Listing multiples (for smaller numbers), or
3. Using the formula:
$$
\text{LCM}(a, b) = \frac{a \times b}{\text{GCD}(a, b)}
$$

We'll use prime factorization and listing where appropriate.

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✔ Let's solve each:

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#### 1. 4 and 22

- Prime factors:
- 4 = 2 × 2 = $2^2$
- 22 = 2 × 11
- LCM = take highest powers: $2^2$ × 11 = 4 × 11 = 44

✔ Answer: 44

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#### 2. 6 and 24

- 6 = 2 × 3
- 24 = 2³ × 3
- LCM = $2^3$ × 3 = 8 × 3 = 24

✔ Answer: 24

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#### 3. 8 and 6

- 8 = $2^3$
- 6 = 2 × 3
- LCM = $2^3$ × 3 = 8 × 3 = 24

✔ Answer: 24

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#### 4. 3 and 4

- 3 = 3
- 4 = $2^2$
- LCM = $2^2$ × 3 = 4 × 3 = 12

✔ Answer: 12

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#### 5. 10 and 23

- 10 = 2 × 5
- 23 = 23 (prime)
- LCM = 2 × 5 × 23 = 230

✔ Answer: 230

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#### 6. 2 and 4

- 2 = 2
- 4 = $2^2$
- LCM = $2^2$ = 4

✔ Answer: 4

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#### 7. 16 and 24

- 16 = $2^4$
- 24 = $2^3$ × 3
- LCM = $2^4$ × 3 = 16 × 3 = 48

✔ Answer: 48

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#### 8. 20 and 6

- 20 = $2^2$ × 5
- 6 = 2 × 3
- LCM = $2^2$ × 3 × 5 = 4 × 3 × 5 = 60

✔ Answer: 60

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#### 9. 10 and 19

- 10 = 2 × 5
- 19 = 19 (prime)
- LCM = 2 × 5 × 19 = 190

✔ Answer: 190

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#### 10. 14 and 28

- 14 = 2 × 7
- 28 = $2^2$ × 7
- LCM = $2^2$ × 7 = 4 × 7 = 28

✔ Answer: 28

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#### 11. 7 and 3

- 7 = 7
- 3 = 3
- LCM = 7 × 3 = 21

✔ Answer: 21

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#### 12. 4 and 29

- 4 = $2^2$
- 29 = 29 (prime)
- LCM = $2^2$ × 29 = 4 × 29 = 116

✔ Answer: 116

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#### 13. 19 and 9

- 19 = 19 (prime)
- 9 = $3^2$
- LCM = 19 × $3^2$ = 19 × 9 = 171

✔ Answer: 171

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#### 14. 9 and 11

- 9 = $3^2$
- 11 = 11 (prime)
- LCM = $3^2$ × 11 = 9 × 11 = 99

✔ Answer: 99

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✔ Final Answers:

| Problem | Numbers | LCM |
|--------|--------|-----|
| 1 | 4, 22 | 44 |
| 2 | 6, 24 | 24 |
| 3 | 8, 6 | 24 |
| 4 | 3, 4 | 12 |
| 5 | 10, 23 | 230 |
| 6 | 2, 4 | 4 |
| 7 | 16, 24 | 48 |
| 8 | 20, 6 | 60 |
| 9 | 10, 19 | 190 |
| 10 | 14, 28 | 28 |
| 11 | 7, 3 | 21 |
| 12 | 4, 29 | 116 |
| 13 | 19, 9 | 171 |
| 14 | 9, 11 | 99 |

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📝 Summary Tips:

- If one number divides the other, the larger number is the LCM (e.g., 6 and 24 → 24).
- For coprime numbers (no common factors), LCM = product (e.g., 3 and 4 → 12).
- Always break down into prime factors for clarity.

Let me know if you'd like this as a printable answer sheet!