Least Common Multiple (LCM) Worksheets - Free Printable

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Show Answer Key & Explanations Step-by-step solution for: Least Common Multiple (LCM) Worksheets

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Sure! Let’s solve each problem step by step. The Least Common Multiple (LCM) of a set of numbers is the smallest positive number that is divisible by each of the numbers in the set.

We’ll use prime factorization to find the LCM for each problem. Here's how it works:

1. Break each number into its prime factors.
2. For each prime, take the highest power that appears in any of the factorizations.
3. Multiply those highest powers together → that’s your LCM.

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1) LCM(5, 7, 10)

- Prime factors:
- 5 = 5
- 7 = 7
- 10 = 2 × 5

- Highest powers: 2¹, 5¹, 7¹
- LCM = 2 × 5 × 7 = 70

✔ Answer: 70

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2) LCM(6, 8, 9)

- Prime factors:
- 6 = 2 × 3
- 8 = 2³
- 9 = 3²

- Highest powers: 2³, 3²
- LCM = 8 × 9 = 72

✔ Answer: 72

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3) LCM(3, 10, 5)

- Prime factors:
- 3 = 3
- 10 = 2 × 5
- 5 = 5

- Highest powers: 2¹, 3¹, 5¹
- LCM = 2 × 3 × 5 = 30

✔ Answer: 30

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4) LCM(9, 6, 12)

- Prime factors:
- 9 = 3²
- 6 = 2 × 3
- 12 = 2² × 3

- Highest powers: 2², 3²
- LCM = 4 × 9 = 36

✔ Answer: 36

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5) LCM(4, 5, 7)

- Prime factors:
- 4 = 2²
- 5 = 5
- 7 = 7

- Highest powers: 2², 5¹, 7¹
- LCM = 4 × 5 × 7 = 140

✔ Answer: 140

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6) LCM(9, 15, 12)

- Prime factors:
- 9 = 3²
- 15 = 3 × 5
- 12 = 2² × 3

- Highest powers: 2², 3², 5¹
- LCM = 4 × 9 × 5 = 180

✔ Answer: 180

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7) LCM(20, 24, 12)

- Prime factors:
- 20 = 2² × 5
- 24 = 2³ × 3
- 12 = 2² × 3

- Highest powers: 2³, 3¹, 5¹
- LCM = 8 × 3 × 5 = 120

✔ Answer: 120

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8) LCM(15, 10, 4)

- Prime factors:
- 15 = 3 × 5
- 10 = 2 × 5
- 4 = 2²

- Highest powers: 2², 3¹, 5¹
- LCM = 4 × 3 × 5 = 60

✔ Answer: 60

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9) LCM(30, 40, 20)

- Prime factors:
- 30 = 2 × 3 × 5
- 40 = 2³ × 5
- 20 = 2² × 5

- Highest powers: 2³, 3¹, 5¹
- LCM = 8 × 3 × 5 = 120

✔ Answer: 120

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10) LCM(15, 12, 40)

- Prime factors:
- 15 = 3 × 5
- 12 = 2² × 3
- 40 = 2³ × 5

- Highest powers: 2³, 3¹, 5¹
- LCM = 8 × 3 × 5 = 120

✔ Answer: 120

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## ✔ Final Answers:

1) 70
2) 72
3) 30
4) 36
5) 140
6) 180
7) 120
8) 60
9) 120
10) 120

Let me know if you’d like to see an alternative method (like listing multiples) or need a visual explanation!

Parent Tip: Review the logic above to help your child master the concept of lcm worksheets.

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