Math worksheet for finding the least common multiple of number pairs.
Worksheet titled "Find the Least Common Multiple for each number pair" with ten problems listing number pairs and blank spaces for answers, including fields for name, teacher, score, and date.
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Show Answer Key & Explanations
Step-by-step solution for: Fractions Worksheets | Printable Fractions Worksheets for Teachers
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Show Answer Key & Explanations
Step-by-step solution for: Fractions Worksheets | Printable Fractions Worksheets for Teachers
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 lowest common denominator worksheet 5th grade.
