Let's solve each problem step by step to find the
Least Common Multiple (LCM) of each pair of numbers.
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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:
$$
\text{LCM}(a, b) = \frac{a \times b}{\text{GCD}(a, b)}
$$
We’ll use
prime factorization for clarity and efficiency.
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✔ Problem 1: 30, 4
Prime factors:
- 30 = 2 × 3 × 5
- 4 = 2²
Take the highest power of each prime:
- 2², 3¹, 5¹
→ LCM = 2² × 3 × 5 = 4 × 3 × 5 =
60
✔ Answer: 60
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✔ Problem 2: 8, 20
Prime factors:
- 8 = 2³
- 20 = 2² × 5
Highest powers:
- 2³, 5¹
→ LCM = 8 × 5 =
40
✔ Answer: 40
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✔ Problem 3: 10, 5
Prime factors:
- 10 = 2 × 5
- 5 = 5
Highest powers:
- 2¹, 5¹ → LCM = 2 × 5 =
10
✔ Answer: 10
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✔ Problem 4: 6, 12
Prime factors:
- 6 = 2 × 3
- 12 = 2² × 3
Highest powers:
- 2², 3¹ → LCM = 4 × 3 =
12
✔ Answer: 12
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✔ Problem 5: 30, 44
Prime factors:
- 30 = 2 × 3 × 5
- 44 = 2² × 11
Highest powers:
- 2², 3¹, 5¹, 11¹
→ LCM = 4 × 3 × 5 × 11 = 660
✔ Answer: 660
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✔ Problem 6: 8, 6
Prime factors:
- 8 = 2³
- 6 = 2 × 3
Highest powers:
- 2³, 3¹ → LCM = 8 × 3 =
24
✔ Answer: 24
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✔ Problem 7: 15, 30
Prime factors:
- 15 = 3 × 5
- 30 = 2 × 3 × 5
Highest powers:
- 2¹, 3¹, 5¹ → LCM = 2 × 3 × 5 =
30
✔ Answer: 30
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✔ Problem 8: 6, 15
Prime factors:
- 6 = 2 × 3
- 15 = 3 × 5
Highest powers:
- 2¹, 3¹, 5¹ → LCM = 2 × 3 × 5 =
30
✔ Answer: 30
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✔ Final Answers:
1. 30, 4 →
60
2. 8, 20 →
40
3. 10, 5 →
10
4. 6, 12 →
12
5. 30, 44 →
660
6. 8, 6 →
24
7. 15, 30 →
30
8. 6, 15 →
30
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Let me know if you'd like a printable version or explanation using another method (like listing multiples)!
Parent Tip: Review the logic above to help your child master the concept of least common multiple worksheet 6th grade.
