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 the LCM using:
-
Prime factorization, or
-
Listing multiples, or
- Using the formula:
$$
\text{LCM}(a, b) = \frac{a \times b}{\text{GCF}(a, b)}
$$
We'll use prime factorization for accuracy and efficiency.
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Now let’s solve each pair:
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1.
2, 4
- Prime factors:
- 2 = 2
- 4 = 2²
- Take the highest power of each prime: 2² =
4
-
✔ LCM = 4
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2.
20, 24
- 20 = 2² × 5
- 24 = 2³ × 3
- Highest powers: 2³ × 3 × 5 = 8 × 3 × 5 =
120
-
✔ LCM = 120
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3.
30, 24
- 30 = 2 × 3 × 5
- 24 = 2³ × 3
- Highest powers: 2³ × 3 × 5 = 8 × 3 × 5 =
120
-
✔ LCM = 120
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4.
30, 4
- 30 = 2 × 3 × 5
- 4 = 2²
- Highest powers: 2² × 3 × 5 = 4 × 3 × 5 =
60
-
✔ LCM = 60
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5.
15, 10
- 15 = 3 × 5
- 10 = 2 × 5
- Highest powers: 2 × 3 × 5 =
30
-
✔ LCM = 30
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6.
20, 3
- 20 = 2² × 5
- 3 = 3
- No common factors → multiply: 20 × 3 =
60
-
✔ LCM = 60
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7.
12, 60
- 12 = 2² × 3
- 60 = 2² × 3 × 5
- Highest powers: 2² × 3 × 5 =
60
-
✔ LCM = 60
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8.
15, 20
- 15 = 3 × 5
- 20 = 2² × 5
- Highest powers: 2² × 3 × 5 = 4 × 3 × 5 =
60
-
✔ LCM = 60
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9.
8, 15
- 8 = 2³
- 15 = 3 × 5
- No common factors → 8 × 15 =
120
-
✔ LCM = 120
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10.
24, 30
- 24 = 2³ × 3
- 30 = 2 × 3 × 5
- Highest powers: 2³ × 3 × 5 = 8 × 3 × 5 =
120
-
✔ LCM = 120
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✔ Final Answers:
| Pair | LCM |
|------------|------|
| 2, 4 | 4 |
| 20, 24 | 120 |
| 30, 24 | 120 |
| 30, 4 | 60 |
| 15, 10 | 30 |
| 20, 3 | 60 |
| 12, 60 | 60 |
| 15, 20 | 60 |
| 8, 15 | 120 |
| 24, 30 | 120 |
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You can now fill these in on the worksheet!
Let me know if you'd like a printable version or explanation for any specific problem!
Parent Tip: Review the logic above to help your child master the concept of least common multiple worksheet 6th grade.
