Math worksheet for finding the least common multiple (LCM) of two numbers, ideal for classroom practice.

Worksheet titled "Least Common Multiple of Two Numbers" with 10 problems asking to find the LCM of pairs of numbers, labeled ES1.

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To solve the problem of finding the least common multiple (LCM) of each pair of numbers, we will use the relationship between the greatest common divisor (GCD) and the LCM. The formula is:

\[
\text{LCM}(a, b) = \frac{|a \cdot b|}{\text{GCD}(a, b)}
\]

We will calculate the LCM for each pair step by step.

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1) LCM(8, 12)

- Prime factorization:
- \(8 = 2^3\)
- \(12 = 2^2 \cdot 3\)

- GCD:
- The common prime factors are \(2^2 = 4\).

- LCM:
\[
\text{LCM}(8, 12) = \frac{8 \cdot 12}{\text{GCD}(8, 12)} = \frac{96}{4} = 24
\]

Answer: \(\boxed{24}\)

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2) LCM(20, 16)

- Prime factorization:
- \(20 = 2^2 \cdot 5\)
- \(16 = 2^4\)

- GCD:
- The common prime factors are \(2^2 = 4\).

- LCM:
\[
\text{LCM}(20, 16) = \frac{20 \cdot 16}{\text{GCD}(20, 16)} = \frac{320}{4} = 80
\]

Answer: \(\boxed{80}\)

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3) LCM(22, 6)

- Prime factorization:
- \(22 = 2 \cdot 11\)
- \(6 = 2 \cdot 3\)

- GCD:
- The common prime factor is \(2\).

- LCM:
\[
\text{LCM}(22, 6) = \frac{22 \cdot 6}{\text{GCD}(22, 6)} = \frac{132}{2} = 66
\]

Answer: \(\boxed{66}\)

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4) LCM(14, 4)

- Prime factorization:
- \(14 = 2 \cdot 7\)
- \(4 = 2^2\)

- GCD:
- The common prime factor is \(2\).

- LCM:
\[
\text{LCM}(14, 4) = \frac{14 \cdot 4}{\text{GCD}(14, 4)} = \frac{56}{2} = 28
\]

Answer: \(\boxed{28}\)

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5) LCM(12, 24)

- Prime factorization:
- \(12 = 2^2 \cdot 3\)
- \(24 = 2^3 \cdot 3\)

- GCD:
- The common prime factors are \(2^2 \cdot 3 = 12\).

- LCM:
\[
\text{LCM}(12, 24) = \frac{12 \cdot 24}{\text{GCD}(12, 24)} = \frac{288}{12} = 24
\]

Answer: \(\boxed{24}\)

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6) LCM(24, 6)

- Prime factorization:
- \(24 = 2^3 \cdot 3\)
- \(6 = 2 \cdot 3\)

- GCD:
- The common prime factors are \(2 \cdot 3 = 6\).

- LCM:
\[
\text{LCM}(24, 6) = \frac{24 \cdot 6}{\text{GCD}(24, 6)} = \frac{144}{6} = 24
\]

Answer: \(\boxed{24}\)

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7) LCM(15, 9)

- Prime factorization:
- \(15 = 3 \cdot 5\)
- \(9 = 3^2\)

- GCD:
- The common prime factor is \(3\).

- LCM:
\[
\text{LCM}(15, 9) = \frac{15 \cdot 9}{\text{GCD}(15, 9)} = \frac{135}{3} = 45
\]

Answer: \(\boxed{45}\)

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8) LCM(5, 20)

- Prime factorization:
- \(5 = 5\)
- \(20 = 2^2 \cdot 5\)

- GCD:
- The common prime factor is \(5\).

- LCM:
\[
\text{LCM}(5, 20) = \frac{5 \cdot 20}{\text{GCD}(5, 20)} = \frac{100}{5} = 20
\]

Answer: \(\boxed{20}\)

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9) LCM(24, 14)

- Prime factorization:
- \(24 = 2^3 \cdot 3\)
- \(14 = 2 \cdot 7\)

- GCD:
- The common prime factor is \(2\).

- LCM:
\[
\text{LCM}(24, 14) = \frac{24 \cdot 14}{\text{GCD}(24, 14)} = \frac{336}{2} = 168
\]

Answer: \(\boxed{168}\)

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10) LCM(10, 8)

- Prime factorization:
- \(10 = 2 \cdot 5\)
- \(8 = 2^3\)

- GCD:
- The common prime factor is \(2\).

- LCM:
\[
\text{LCM}(10, 8) = \frac{10 \cdot 8}{\text{GCD}(10, 8)} = \frac{80}{2} = 40
\]

Answer: \(\boxed{40}\)

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Final Answers

1. \(\boxed{24}\)
2. \(\boxed{80}\)
3. \(\boxed{66}\)
4. \(\boxed{28}\)
5. \(\boxed{24}\)
6. \(\boxed{24}\)
7. \(\boxed{45}\)
8. \(\boxed{20}\)
9. \(\boxed{168}\)
10. \(\boxed{40}\)

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