Math worksheet for finding LCM and GCF of number pairs.

To solve the problem, we need to find both the Least Common Multiple (LCM) and the Greatest Common Factor (GCF) for each pair of numbers. Let's go through each pair step by step.

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1. Pair: 16, 10

#### GCF (Greatest Common Factor):
- Prime factorization:
- \( 16 = 2^4 \)
- \( 10 = 2 \times 5 \)
- Common factors: The only common factor is \( 2 \).
- GCF: \( 2 \)

#### LCM (Least Common Multiple):
- LCM is found by taking the highest power of all prime factors involved.
- From \( 16 = 2^4 \) and \( 10 = 2 \times 5 \):
- Highest power of \( 2 \): \( 2^4 \)
- Highest power of \( 5 \): \( 5^1 \)
- LCM: \( 2^4 \times 5 = 16 \times 5 = 80 \)

Result:
- LCM: \( 80 \)
- GCF: \( 2 \)

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2. Pair: 14, 6

#### GCF (Greatest Common Factor):
- Prime factorization:
- \( 14 = 2 \times 7 \)
- \( 6 = 2 \times 3 \)
- Common factors: The only common factor is \( 2 \).
- GCF: \( 2 \)

#### LCM (Least Common Multiple):
- LCM is found by taking the highest power of all prime factors involved.
- From \( 14 = 2 \times 7 \) and \( 6 = 2 \times 3 \):
- Highest power of \( 2 \): \( 2^1 \)
- Highest power of \( 3 \): \( 3^1 \)
- Highest power of \( 7 \): \( 7^1 \)
- LCM: \( 2 \times 3 \times 7 = 42 \)

Result:
- LCM: \( 42 \)
- GCF: \( 2 \)

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3. Pair: 3, 27

#### GCF (Greatest Common Factor):
- Prime factorization:
- \( 3 = 3 \)
- \( 27 = 3^3 \)
- Common factors: The common factor is \( 3 \).
- GCF: \( 3 \)

#### LCM (Least Common Multiple):
- LCM is found by taking the highest power of all prime factors involved.
- From \( 3 = 3 \) and \( 27 = 3^3 \):
- Highest power of \( 3 \): \( 3^3 \)
- LCM: \( 3^3 = 27 \)

Result:
- LCM: \( 27 \)
- GCF: \( 3 \)

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4. Pair: 6, 14

#### GCF (Greatest Common Factor):
- Prime factorization:
- \( 6 = 2 \times 3 \)
- \( 14 = 2 \times 7 \)
- Common factors: The only common factor is \( 2 \).
- GCF: \( 2 \)

#### LCM (Least Common Multiple):
- LCM is found by taking the highest power of all prime factors involved.
- From \( 6 = 2 \times 3 \) and \( 14 = 2 \times 7 \):
- Highest power of \( 2 \): \( 2^1 \)
- Highest power of \( 3 \): \( 3^1 \)
- Highest power of \( 7 \): \( 7^1 \)
- LCM: \( 2 \times 3 \times 7 = 42 \)

Result:
- LCM: \( 42 \)
- GCF: \( 2 \)

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5. Pair: 16, 5

#### GCF (Greatest Common Factor):
- Prime factorization:
- \( 16 = 2^4 \)
- \( 5 = 5 \)
- Common factors: There are no common factors other than \( 1 \).
- GCF: \( 1 \)

#### LCM (Least Common Multiple):
- LCM is found by taking the highest power of all prime factors involved.
- From \( 16 = 2^4 \) and \( 5 = 5 \):
- Highest power of \( 2 \): \( 2^4 \)
- Highest power of \( 5 \): \( 5^1 \)
- LCM: \( 2^4 \times 5 = 16 \times 5 = 80 \)

Result:
- LCM: \( 80 \)
- GCF: \( 1 \)

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6. Pair: 8, 12

#### GCF (Greatest Common Factor):
- Prime factorization:
- \( 8 = 2^3 \)
- \( 12 = 2^2 \times 3 \)
- Common factors: The common factor is \( 2^2 = 4 \).
- GCF: \( 4 \)

#### LCM (Least Common Multiple):
- LCM is found by taking the highest power of all prime factors involved.
- From \( 8 = 2^3 \) and \( 12 = 2^2 \times 3 \):
- Highest power of \( 2 \): \( 2^3 \)
- Highest power of \( 3 \): \( 3^1 \)
- LCM: \( 2^3 \times 3 = 8 \times 3 = 24 \)

Result:
- LCM: \( 24 \)
- GCF: \( 4 \)

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7. Pair: 16, 6

#### GCF (Greatest Common Factor):
- Prime factorization:
- \( 16 = 2^4 \)
- \( 6 = 2 \times 3 \)
- Common factors: The only common factor is \( 2 \).
- GCF: \( 2 \)

#### LCM (Least Common Multiple):
- LCM is found by taking the highest power of all prime factors involved.
- From \( 16 = 2^4 \) and \( 6 = 2 \times 3 \):
- Highest power of \( 2 \): \( 2^4 \)
- Highest power of \( 3 \): \( 3^1 \)
- LCM: \( 2^4 \times 3 = 16 \times 3 = 48 \)

Result:
- LCM: \( 48 \)
- GCF: \( 2 \)

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8. Pair: 8, 3

#### GCF (Greatest Common Factor):
- Prime factorization:
- \( 8 = 2^3 \)
- \( 3 = 3 \)
- Common factors: There are no common factors other than \( 1 \).
- GCF: \( 1 \)

#### LCM (Least Common Multiple):
- LCM is found by taking the highest power of all prime factors involved.
- From \( 8 = 2^3 \) and \( 3 = 3 \):
- Highest power of \( 2 \): \( 2^3 \)
- Highest power of \( 3 \): \( 3^1 \)
- LCM: \( 2^3 \times 3 = 8 \times 3 = 24 \)

Result:
- LCM: \( 24 \)
- GCF: \( 1 \)

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Final Answers:

| Pair | LCM | GCF |
|----------|-------|-------|
| 16, 10 | 80 | 2 |
| 14, 6 | 42 | 2 |
| 3, 27 | 27 | 3 |
| 6, 14 | 42 | 2 |
| 16, 5 | 80 | 1 |
| 8, 12 | 24 | 4 |
| 16, 6 | 48 | 2 |
| 8, 3 | 24 | 1 |

\boxed{
\begin{array}{c|c|c}
\text{Pair} & \text{LCM} & \text{GCF} \\
\hline
16, 10 & 80 & 2 \\
14, 6 & 42 & 2 \\
3, 27 & 27 & 3 \\
6, 14 & 42 & 2 \\
16, 5 & 80 & 1 \\
8, 12 & 24 & 4 \\
16, 6 & 48 & 2 \\
8, 3 & 24 & 1 \\
\end{array}
}