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!
Parent Tip: Review the logic above to help your child master the concept of least common multiples worksheet 5th grade.