Let's solve each of the
Least Common Multiple (LCM) problems step by step.
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🔷 What is LCM?
The
Least Common Multiple of two numbers is the smallest number that is a multiple of both numbers.
We can find LCM using:
-
Prime factorization, or
-
Division method, or
-
Using the formula:
$$
\text{LCM}(a, b) = \frac{a \times b}{\text{GCD}(a, b)}
$$
We’ll use
prime factorization and
GCD method where appropriate.
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✔ Problem 1: 8 and 48
- 8 = 2³
- 48 = 2⁴ × 3
- LCM = 2⁴ × 3 = 16 × 3 =
48
✔ Answer: 48
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✔ Problem 2: 11 and 44
- 11 is prime
- 44 = 2² × 11
- LCM = 2² × 11 = 4 × 11 =
44
✔ Answer: 44
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✔ Problem 3: 6 and 36
- 6 = 2 × 3
- 36 = 2² × 3²
- LCM = 2² × 3² = 4 × 9 =
36
✔ Answer: 36
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✔ Problem 4: 21 and 33
- 21 = 3 × 7
- 33 = 3 × 11
- LCM = 3 × 7 × 11 =
231
✔ Answer: 231
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✔ Problem 5: 15 and 55
- 15 = 3 × 5
- 55 = 5 × 11
- LCM = 3 × 5 × 11 =
165
✔ Answer: 165
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✔ Problem 6: 20 and 35
- 20 = 2² × 5
- 35 = 5 × 7
- LCM = 2² × 5 × 7 = 4 × 5 × 7 =
140
✔ Answer: 140
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✔ Problem 7: 6 and 66
- 6 = 2 × 3
- 66 = 2 × 3 × 11
- LCM = 2 × 3 × 11 =
66
✔ Answer: 66
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✔ Problem 8: 12 and 39
- 12 = 2² × 3
- 39 = 3 × 13
- LCM = 2² × 3 × 13 = 4 × 3 × 13 =
156
✔ Answer: 156
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✔ Problem 9: 22 and 33
- 22 = 2 × 11
- 33 = 3 × 11
- LCM = 2 × 3 × 11 =
66
✔ Answer: 66
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✔ Problem 10: 26 and 39
- 26 = 2 × 13
- 39 = 3 × 13
- LCM = 2 × 3 × 13 =
78
✔ Answer: 78
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✔ Problem 11: 19 and 57
- 19 is prime
- 57 = 3 × 19
- LCM = 3 × 19 =
57
✔ Answer: 57
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✔ Problem 12: 12 and 28
- 12 = 2² × 3
- 28 = 2² × 7
- LCM = 2² × 3 × 7 = 4 × 3 × 7 =
84
✔ Answer: 84
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📌 Final Answers:
| Numbers | LCM |
|----------------|-------|
| 8 and 48 | 48 |
| 11 and 44 | 44 |
| 6 and 36 | 36 |
| 21 and 33 | 231 |
| 15 and 55 | 165 |
| 20 and 35 | 140 |
| 6 and 66 | 66 |
| 12 and 39 | 156 |
| 22 and 33 | 66 |
| 26 and 39 | 78 |
| 19 and 57 | 57 |
| 12 and 28 | 84 |
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Let me know if you'd like this in printable format or with steps for each! 😊
Parent Tip: Review the logic above to help your child master the concept of lcm practice worksheet.
