Factors Worksheets | Printable Factors and Multiples Worksheets - Free Printable
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Step-by-step solution for: Factors Worksheets | Printable Factors and Multiples Worksheets
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Show Answer Key & Explanations
Step-by-step solution for: Factors Worksheets | Printable Factors and Multiples Worksheets
To solve the problem of finding the Least Common Multiple (LCM) for each number pair, we will use the following steps:
1. Prime Factorization: Break down each number into its prime factors.
2. Identify All Prime Factors: List all the prime factors that appear in either number.
3. Take the Highest Powers: For each prime factor, take the highest power that appears in the factorizations.
4. Multiply: Multiply these highest powers together to get the LCM.
Let's solve each pair step by step.
---
- Prime Factorization:
- \( 5 = 5 \)
- \( 24 = 2^3 \times 3 \)
- Identify All Prime Factors: \( 2, 3, 5 \)
- Take the Highest Powers:
- \( 2^3 \) (from 24)
- \( 3^1 \) (from 24)
- \( 5^1 \) (from 5)
- Multiply:
\[
\text{LCM} = 2^3 \times 3^1 \times 5^1 = 8 \times 3 \times 5 = 120
\]
- Answer: \( 120 \)
---
- Prime Factorization:
- \( 40 = 2^3 \times 5 \)
- \( 20 = 2^2 \times 5 \)
- Identify All Prime Factors: \( 2, 5 \)
- Take the Highest Powers:
- \( 2^3 \) (from 40)
- \( 5^1 \) (from both 40 and 20)
- Multiply:
\[
\text{LCM} = 2^3 \times 5^1 = 8 \times 5 = 40
\]
- Answer: \( 40 \)
---
- Prime Factorization:
- \( 8 = 2^3 \)
- \( 5 = 5 \)
- Identify All Prime Factors: \( 2, 5 \)
- Take the Highest Powers:
- \( 2^3 \) (from 8)
- \( 5^1 \) (from 5)
- Multiply:
\[
\text{LCM} = 2^3 \times 5^1 = 8 \times 5 = 40
\]
- Answer: \( 40 \)
---
- Prime Factorization:
- \( 15 = 3 \times 5 \)
- \( 2 = 2 \)
- Identify All Prime Factors: \( 2, 3, 5 \)
- Take the Highest Powers:
- \( 2^1 \) (from 2)
- \( 3^1 \) (from 15)
- \( 5^1 \) (from 15)
- Multiply:
\[
\text{LCM} = 2^1 \times 3^1 \times 5^1 = 2 \times 3 \times 5 = 30
\]
- Answer: \( 30 \)
---
- Prime Factorization:
- \( 40 = 2^3 \times 5 \)
- \( 2 = 2 \)
- Identify All Prime Factors: \( 2, 5 \)
- Take the Highest Powers:
- \( 2^3 \) (from 40)
- \( 5^1 \) (from 40)
- Multiply:
\[
\text{LCM} = 2^3 \times 5^1 = 8 \times 5 = 40
\]
- Answer: \( 40 \)
---
- Prime Factorization:
- \( 3 = 3 \)
- \( 5 = 5 \)
- Identify All Prime Factors: \( 3, 5 \)
- Take the Highest Powers:
- \( 3^1 \) (from 3)
- \( 5^1 \) (from 5)
- Multiply:
\[
\text{LCM} = 3^1 \times 5^1 = 3 \times 5 = 15
\]
- Answer: \( 15 \)
---
- Prime Factorization:
- \( 8 = 2^3 \)
- \( 4 = 2^2 \)
- Identify All Prime Factors: \( 2 \)
- Take the Highest Powers:
- \( 2^3 \) (from 8)
- Multiply:
\[
\text{LCM} = 2^3 = 8
\]
- Answer: \( 8 \)
---
- Prime Factorization:
- \( 4 = 2^2 \)
- \( 5 = 5 \)
- Identify All Prime Factors: \( 2, 5 \)
- Take the Highest Powers:
- \( 2^2 \) (from 4)
- \( 5^1 \) (from 5)
- Multiply:
\[
\text{LCM} = 2^2 \times 5^1 = 4 \times 5 = 20
\]
- Answer: \( 20 \)
---
- Prime Factorization:
- \( 2 = 2 \)
- \( 12 = 2^2 \times 3 \)
- Identify All Prime Factors: \( 2, 3 \)
- Take the Highest Powers:
- \( 2^2 \) (from 12)
- \( 3^1 \) (from 12)
- Multiply:
\[
\text{LCM} = 2^2 \times 3^1 = 4 \times 3 = 12
\]
- Answer: \( 12 \)
---
- Prime Factorization:
- \( 24 = 2^3 \times 3 \)
- \( 3 = 3 \)
- Identify All Prime Factors: \( 2, 3 \)
- Take the Highest Powers:
- \( 2^3 \) (from 24)
- \( 3^1 \) (from both 24 and 3)
- Multiply:
\[
\text{LCM} = 2^3 \times 3^1 = 8 \times 3 = 24
\]
- Answer: \( 24 \)
---
\[
\boxed{
\begin{array}{ll}
1) & 120 \\
2) & 40 \\
3) & 40 \\
4) & 30 \\
5) & 40 \\
6) & 15 \\
7) & 8 \\
8) & 20 \\
9) & 12 \\
10) & 24 \\
\end{array}
}
\]
Steps to Find LCM:
1. Prime Factorization: Break down each number into its prime factors.
2. Identify All Prime Factors: List all the prime factors that appear in either number.
3. Take the Highest Powers: For each prime factor, take the highest power that appears in the factorizations.
4. Multiply: Multiply these highest powers together to get the LCM.
Let's solve each pair step by step.
---
1. \( 5, 24 \)
- Prime Factorization:
- \( 5 = 5 \)
- \( 24 = 2^3 \times 3 \)
- Identify All Prime Factors: \( 2, 3, 5 \)
- Take the Highest Powers:
- \( 2^3 \) (from 24)
- \( 3^1 \) (from 24)
- \( 5^1 \) (from 5)
- Multiply:
\[
\text{LCM} = 2^3 \times 3^1 \times 5^1 = 8 \times 3 \times 5 = 120
\]
- Answer: \( 120 \)
---
2. \( 40, 20 \)
- Prime Factorization:
- \( 40 = 2^3 \times 5 \)
- \( 20 = 2^2 \times 5 \)
- Identify All Prime Factors: \( 2, 5 \)
- Take the Highest Powers:
- \( 2^3 \) (from 40)
- \( 5^1 \) (from both 40 and 20)
- Multiply:
\[
\text{LCM} = 2^3 \times 5^1 = 8 \times 5 = 40
\]
- Answer: \( 40 \)
---
3. \( 8, 5 \)
- Prime Factorization:
- \( 8 = 2^3 \)
- \( 5 = 5 \)
- Identify All Prime Factors: \( 2, 5 \)
- Take the Highest Powers:
- \( 2^3 \) (from 8)
- \( 5^1 \) (from 5)
- Multiply:
\[
\text{LCM} = 2^3 \times 5^1 = 8 \times 5 = 40
\]
- Answer: \( 40 \)
---
4. \( 15, 2 \)
- Prime Factorization:
- \( 15 = 3 \times 5 \)
- \( 2 = 2 \)
- Identify All Prime Factors: \( 2, 3, 5 \)
- Take the Highest Powers:
- \( 2^1 \) (from 2)
- \( 3^1 \) (from 15)
- \( 5^1 \) (from 15)
- Multiply:
\[
\text{LCM} = 2^1 \times 3^1 \times 5^1 = 2 \times 3 \times 5 = 30
\]
- Answer: \( 30 \)
---
5. \( 40, 2 \)
- Prime Factorization:
- \( 40 = 2^3 \times 5 \)
- \( 2 = 2 \)
- Identify All Prime Factors: \( 2, 5 \)
- Take the Highest Powers:
- \( 2^3 \) (from 40)
- \( 5^1 \) (from 40)
- Multiply:
\[
\text{LCM} = 2^3 \times 5^1 = 8 \times 5 = 40
\]
- Answer: \( 40 \)
---
6. \( 3, 5 \)
- Prime Factorization:
- \( 3 = 3 \)
- \( 5 = 5 \)
- Identify All Prime Factors: \( 3, 5 \)
- Take the Highest Powers:
- \( 3^1 \) (from 3)
- \( 5^1 \) (from 5)
- Multiply:
\[
\text{LCM} = 3^1 \times 5^1 = 3 \times 5 = 15
\]
- Answer: \( 15 \)
---
7. \( 8, 4 \)
- Prime Factorization:
- \( 8 = 2^3 \)
- \( 4 = 2^2 \)
- Identify All Prime Factors: \( 2 \)
- Take the Highest Powers:
- \( 2^3 \) (from 8)
- Multiply:
\[
\text{LCM} = 2^3 = 8
\]
- Answer: \( 8 \)
---
8. \( 4, 5 \)
- Prime Factorization:
- \( 4 = 2^2 \)
- \( 5 = 5 \)
- Identify All Prime Factors: \( 2, 5 \)
- Take the Highest Powers:
- \( 2^2 \) (from 4)
- \( 5^1 \) (from 5)
- Multiply:
\[
\text{LCM} = 2^2 \times 5^1 = 4 \times 5 = 20
\]
- Answer: \( 20 \)
---
9. \( 2, 12 \)
- Prime Factorization:
- \( 2 = 2 \)
- \( 12 = 2^2 \times 3 \)
- Identify All Prime Factors: \( 2, 3 \)
- Take the Highest Powers:
- \( 2^2 \) (from 12)
- \( 3^1 \) (from 12)
- Multiply:
\[
\text{LCM} = 2^2 \times 3^1 = 4 \times 3 = 12
\]
- Answer: \( 12 \)
---
10. \( 24, 3 \)
- Prime Factorization:
- \( 24 = 2^3 \times 3 \)
- \( 3 = 3 \)
- Identify All Prime Factors: \( 2, 3 \)
- Take the Highest Powers:
- \( 2^3 \) (from 24)
- \( 3^1 \) (from both 24 and 3)
- Multiply:
\[
\text{LCM} = 2^3 \times 3^1 = 8 \times 3 = 24
\]
- Answer: \( 24 \)
---
Final Answers:
\[
\boxed{
\begin{array}{ll}
1) & 120 \\
2) & 40 \\
3) & 40 \\
4) & 30 \\
5) & 40 \\
6) & 15 \\
7) & 8 \\
8) & 20 \\
9) & 12 \\
10) & 24 \\
\end{array}
}
\]
Parent Tip: Review the logic above to help your child master the concept of multiple and factors worksheet.
