Printable LCM worksheet for practicing finding least common multiples.

Let's solve each problem step by step to find the Least Common Multiple (LCM) of the given pairs 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:
- Listing multiples, or
- Prime factorization method

We’ll use the prime factorization method for efficiency.

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✔ Problem 1: 6 and 9

Prime factors:
- 6 = 2 × 3
- 9 = 3²

Take the highest powers of all primes:
- 2¹ × 3² = 2 × 9 = 18

✔ LCM = 18

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✔ Problem 2: 12 and 2

Prime factors:
- 12 = 2² × 3
- 2 = 2¹

Highest powers:
- 2² × 3 = 4 × 3 = 12

✔ LCM = 12

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✔ Problem 3: 9 and 15

Prime factors:
- 9 = 3²
- 15 = 3 × 5

Highest powers:
- 3² × 5 = 9 × 5 = 45

✔ LCM = 45

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✔ Problem 4: 5 and 20

Prime factors:
- 5 = 5¹
- 20 = 2² × 5¹

Highest powers:
- 2² × 5¹ = 4 × 5 = 20

✔ LCM = 20

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✔ Problem 5: 9 and 6

Prime factors:
- 9 = 3²
- 6 = 2 × 3

Highest powers:
- 2¹ × 3² = 2 × 9 = 18

✔ LCM = 18

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✔ Problem 6: 3 and 5

Both are prime:
- 3 = 3¹
- 5 = 5¹

LCM = 3 × 5 = 15

✔ LCM = 15

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✔ Problem 7: 10 and 5

Prime factors:
- 10 = 2 × 5
- 5 = 5¹

Highest powers:
- 2¹ × 5¹ = 2 × 5 = 10

✔ LCM = 10

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✔ Problem 8: 20 and 5

Prime factors:
- 20 = 2² × 5
- 5 = 5¹

Highest powers:
- 2² × 5¹ = 4 × 5 = 20

✔ LCM = 20

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✔ Problem 9: 6 and 12

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

Highest powers:
- 2² × 3 = 4 × 3 = 12

✔ LCM = 12

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✔ Problem 10: 10 and 20

Prime factors:
- 10 = 2 × 5
- 20 = 2² × 5

Highest powers:
- 2² × 5 = 4 × 5 = 20

✔ LCM = 20

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✔ Final Answers:

1) 6 and 9 = 18
2) 12 and 2 = 12
3) 9 and 15 = 45
4) 5 and 20 = 20
5) 9 and 6 = 18
6) 3 and 5 = 15
7) 10 and 5 = 10
8) 20 and 5 = 20
9) 6 and 12 = 12
10) 10 and 20 = 20

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Let me know if you'd like this in a printable format or explained with listing multiples!