LCM of Three Numbers Worksheets - Free Printable
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Step-by-step solution for: LCM of Three Numbers Worksheets
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Show Answer Key & Explanations
Step-by-step solution for: LCM of Three Numbers Worksheets
To solve the problem of finding the Least Common Multiple (LCM) of each set of numbers, we will use the prime factorization method. The LCM is the smallest number that is a multiple of all the given numbers. Here's how we can approach each problem step by step:
---
- Prime Factorization:
- \( 8 = 2^3 \)
- \( 17 = 17^1 \)
- \( 2 = 2^1 \)
- Identify the highest power of each prime factor:
- For \( 2 \): The highest power is \( 2^3 \).
- For \( 17 \): The highest power is \( 17^1 \).
- LCM Calculation:
\[
\text{LCM} = 2^3 \times 17^1 = 8 \times 17 = 136
\]
- Answer:
\[
\boxed{136}
\]
---
- Prime Factorization:
- \( 22 = 2^1 \times 11^1 \)
- \( 8 = 2^3 \)
- \( 4 = 2^2 \)
- Identify the highest power of each prime factor:
- For \( 2 \): The highest power is \( 2^3 \).
- For \( 11 \): The highest power is \( 11^1 \).
- LCM Calculation:
\[
\text{LCM} = 2^3 \times 11^1 = 8 \times 11 = 88
\]
- Answer:
\[
\boxed{88}
\]
---
- Prime Factorization:
- \( 12 = 2^2 \times 3^1 \)
- \( 36 = 2^2 \times 3^2 \)
- \( 72 = 2^3 \times 3^2 \)
- Identify the highest power of each prime factor:
- For \( 2 \): The highest power is \( 2^3 \).
- For \( 3 \): The highest power is \( 3^2 \).
- LCM Calculation:
\[
\text{LCM} = 2^3 \times 3^2 = 8 \times 9 = 72
\]
- Answer:
\[
\boxed{72}
\]
---
- Prime Factorization:
- \( 3 = 3^1 \)
- \( 37 = 37^1 \)
- \( 15 = 3^1 \times 5^1 \)
- Identify the highest power of each prime factor:
- For \( 3 \): The highest power is \( 3^1 \).
- For \( 5 \): The highest power is \( 5^1 \).
- For \( 37 \): The highest power is \( 37^1 \).
- LCM Calculation:
\[
\text{LCM} = 3^1 \times 5^1 \times 37^1 = 3 \times 5 \times 37 = 555
\]
- Answer:
\[
\boxed{555}
\]
---
- Prime Factorization:
- \( 5 = 5^1 \)
- \( 4 = 2^2 \)
- \( 10 = 2^1 \times 5^1 \)
- Identify the highest power of each prime factor:
- For \( 2 \): The highest power is \( 2^2 \).
- For \( 5 \): The highest power is \( 5^1 \).
- LCM Calculation:
\[
\text{LCM} = 2^2 \times 5^1 = 4 \times 5 = 20
\]
- Answer:
\[
\boxed{20}
\]
---
- Prime Factorization:
- \( 18 = 2^1 \times 3^2 \)
- \( 45 = 3^2 \times 5^1 \)
- \( 90 = 2^1 \times 3^2 \times 5^1 \)
- Identify the highest power of each prime factor:
- For \( 2 \): The highest power is \( 2^1 \).
- For \( 3 \): The highest power is \( 3^2 \).
- For \( 5 \): The highest power is \( 5^1 \).
- LCM Calculation:
\[
\text{LCM} = 2^1 \times 3^2 \times 5^1 = 2 \times 9 \times 5 = 90
\]
- Answer:
\[
\boxed{90}
\]
---
- Prime Factorization:
- \( 42 = 2^1 \times 3^1 \times 7^1 \)
- \( 21 = 3^1 \times 7^1 \)
- \( 34 = 2^1 \times 17^1 \)
- Identify the highest power of each prime factor:
- For \( 2 \): The highest power is \( 2^1 \).
- For \( 3 \): The highest power is \( 3^1 \).
- For \( 7 \): The highest power is \( 7^1 \).
- For \( 17 \): The highest power is \( 17^1 \).
- LCM Calculation:
\[
\text{LCM} = 2^1 \times 3^1 \times 7^1 \times 17^1 = 2 \times 3 \times 7 \times 17 = 714
\]
- Answer:
\[
\boxed{714}
\]
---
- Prime Factorization:
- \( 50 = 2^1 \times 5^2 \)
- \( 20 = 2^2 \times 5^1 \)
- \( 40 = 2^3 \times 5^1 \)
- Identify the highest power of each prime factor:
- For \( 2 \): The highest power is \( 2^3 \).
- For \( 5 \): The highest power is \( 5^2 \).
- LCM Calculation:
\[
\text{LCM} = 2^3 \times 5^2 = 8 \times 25 = 200
\]
- Answer:
\[
\boxed{200}
\]
---
- Prime Factorization:
- \( 56 = 2^3 \times 7^1 \)
- \( 14 = 2^1 \times 7^1 \)
- \( 8 = 2^3 \)
- Identify the highest power of each prime factor:
- For \( 2 \): The highest power is \( 2^3 \).
- For \( 7 \): The highest power is \( 7^1 \).
- LCM Calculation:
\[
\text{LCM} = 2^3 \times 7^1 = 8 \times 7 = 56
\]
- Answer:
\[
\boxed{56}
\]
---
- Prime Factorization:
- \( 33 = 3^1 \times 11^1 \)
- \( 12 = 2^2 \times 3^1 \)
- \( 3 = 3^1 \)
- Identify the highest power of each prime factor:
- For \( 2 \): The highest power is \( 2^2 \).
- For \( 3 \): The highest power is \( 3^1 \).
- For \( 11 \): The highest power is \( 11^1 \).
- LCM Calculation:
\[
\text{LCM} = 2^2 \times 3^1 \times 11^1 = 4 \times 3 \times 11 = 132
\]
- Answer:
\[
\boxed{132}
\]
---
\[
\begin{aligned}
1) & \quad \text{LCM}(8, 17, 2) = \boxed{136} \\
2) & \quad \text{LCM}(22, 8, 4) = \boxed{88} \\
3) & \quad \text{LCM}(12, 36, 72) = \boxed{72} \\
4) & \quad \text{LCM}(3, 37, 15) = \boxed{555} \\
5) & \quad \text{LCM}(5, 4, 10) = \boxed{20} \\
6) & \quad \text{LCM}(18, 45, 90) = \boxed{90} \\
7) & \quad \text{LCM}(42, 21, 34) = \boxed{714} \\
8) & \quad \text{LCM}(50, 20, 40) = \boxed{200} \\
9) & \quad \text{LCM}(56, 14, 8) = \boxed{56} \\
10) & \quad \text{LCM}(33, 12, 3) = \boxed{132}
\end{aligned}
\]
---
1. LCM(8, 17, 2)
- Prime Factorization:
- \( 8 = 2^3 \)
- \( 17 = 17^1 \)
- \( 2 = 2^1 \)
- Identify the highest power of each prime factor:
- For \( 2 \): The highest power is \( 2^3 \).
- For \( 17 \): The highest power is \( 17^1 \).
- LCM Calculation:
\[
\text{LCM} = 2^3 \times 17^1 = 8 \times 17 = 136
\]
- Answer:
\[
\boxed{136}
\]
---
2. LCM(22, 8, 4)
- Prime Factorization:
- \( 22 = 2^1 \times 11^1 \)
- \( 8 = 2^3 \)
- \( 4 = 2^2 \)
- Identify the highest power of each prime factor:
- For \( 2 \): The highest power is \( 2^3 \).
- For \( 11 \): The highest power is \( 11^1 \).
- LCM Calculation:
\[
\text{LCM} = 2^3 \times 11^1 = 8 \times 11 = 88
\]
- Answer:
\[
\boxed{88}
\]
---
3. LCM(12, 36, 72)
- Prime Factorization:
- \( 12 = 2^2 \times 3^1 \)
- \( 36 = 2^2 \times 3^2 \)
- \( 72 = 2^3 \times 3^2 \)
- Identify the highest power of each prime factor:
- For \( 2 \): The highest power is \( 2^3 \).
- For \( 3 \): The highest power is \( 3^2 \).
- LCM Calculation:
\[
\text{LCM} = 2^3 \times 3^2 = 8 \times 9 = 72
\]
- Answer:
\[
\boxed{72}
\]
---
4. LCM(3, 37, 15)
- Prime Factorization:
- \( 3 = 3^1 \)
- \( 37 = 37^1 \)
- \( 15 = 3^1 \times 5^1 \)
- Identify the highest power of each prime factor:
- For \( 3 \): The highest power is \( 3^1 \).
- For \( 5 \): The highest power is \( 5^1 \).
- For \( 37 \): The highest power is \( 37^1 \).
- LCM Calculation:
\[
\text{LCM} = 3^1 \times 5^1 \times 37^1 = 3 \times 5 \times 37 = 555
\]
- Answer:
\[
\boxed{555}
\]
---
5. LCM(5, 4, 10)
- Prime Factorization:
- \( 5 = 5^1 \)
- \( 4 = 2^2 \)
- \( 10 = 2^1 \times 5^1 \)
- Identify the highest power of each prime factor:
- For \( 2 \): The highest power is \( 2^2 \).
- For \( 5 \): The highest power is \( 5^1 \).
- LCM Calculation:
\[
\text{LCM} = 2^2 \times 5^1 = 4 \times 5 = 20
\]
- Answer:
\[
\boxed{20}
\]
---
6. LCM(18, 45, 90)
- Prime Factorization:
- \( 18 = 2^1 \times 3^2 \)
- \( 45 = 3^2 \times 5^1 \)
- \( 90 = 2^1 \times 3^2 \times 5^1 \)
- Identify the highest power of each prime factor:
- For \( 2 \): The highest power is \( 2^1 \).
- For \( 3 \): The highest power is \( 3^2 \).
- For \( 5 \): The highest power is \( 5^1 \).
- LCM Calculation:
\[
\text{LCM} = 2^1 \times 3^2 \times 5^1 = 2 \times 9 \times 5 = 90
\]
- Answer:
\[
\boxed{90}
\]
---
7. LCM(42, 21, 34)
- Prime Factorization:
- \( 42 = 2^1 \times 3^1 \times 7^1 \)
- \( 21 = 3^1 \times 7^1 \)
- \( 34 = 2^1 \times 17^1 \)
- Identify the highest power of each prime factor:
- For \( 2 \): The highest power is \( 2^1 \).
- For \( 3 \): The highest power is \( 3^1 \).
- For \( 7 \): The highest power is \( 7^1 \).
- For \( 17 \): The highest power is \( 17^1 \).
- LCM Calculation:
\[
\text{LCM} = 2^1 \times 3^1 \times 7^1 \times 17^1 = 2 \times 3 \times 7 \times 17 = 714
\]
- Answer:
\[
\boxed{714}
\]
---
8. LCM(50, 20, 40)
- Prime Factorization:
- \( 50 = 2^1 \times 5^2 \)
- \( 20 = 2^2 \times 5^1 \)
- \( 40 = 2^3 \times 5^1 \)
- Identify the highest power of each prime factor:
- For \( 2 \): The highest power is \( 2^3 \).
- For \( 5 \): The highest power is \( 5^2 \).
- LCM Calculation:
\[
\text{LCM} = 2^3 \times 5^2 = 8 \times 25 = 200
\]
- Answer:
\[
\boxed{200}
\]
---
9. LCM(56, 14, 8)
- Prime Factorization:
- \( 56 = 2^3 \times 7^1 \)
- \( 14 = 2^1 \times 7^1 \)
- \( 8 = 2^3 \)
- Identify the highest power of each prime factor:
- For \( 2 \): The highest power is \( 2^3 \).
- For \( 7 \): The highest power is \( 7^1 \).
- LCM Calculation:
\[
\text{LCM} = 2^3 \times 7^1 = 8 \times 7 = 56
\]
- Answer:
\[
\boxed{56}
\]
---
10. LCM(33, 12, 3)
- Prime Factorization:
- \( 33 = 3^1 \times 11^1 \)
- \( 12 = 2^2 \times 3^1 \)
- \( 3 = 3^1 \)
- Identify the highest power of each prime factor:
- For \( 2 \): The highest power is \( 2^2 \).
- For \( 3 \): The highest power is \( 3^1 \).
- For \( 11 \): The highest power is \( 11^1 \).
- LCM Calculation:
\[
\text{LCM} = 2^2 \times 3^1 \times 11^1 = 4 \times 3 \times 11 = 132
\]
- Answer:
\[
\boxed{132}
\]
---
Final Answers:
\[
\begin{aligned}
1) & \quad \text{LCM}(8, 17, 2) = \boxed{136} \\
2) & \quad \text{LCM}(22, 8, 4) = \boxed{88} \\
3) & \quad \text{LCM}(12, 36, 72) = \boxed{72} \\
4) & \quad \text{LCM}(3, 37, 15) = \boxed{555} \\
5) & \quad \text{LCM}(5, 4, 10) = \boxed{20} \\
6) & \quad \text{LCM}(18, 45, 90) = \boxed{90} \\
7) & \quad \text{LCM}(42, 21, 34) = \boxed{714} \\
8) & \quad \text{LCM}(50, 20, 40) = \boxed{200} \\
9) & \quad \text{LCM}(56, 14, 8) = \boxed{56} \\
10) & \quad \text{LCM}(33, 12, 3) = \boxed{132}
\end{aligned}
\]
Parent Tip: Review the logic above to help your child master the concept of least common multiple worksheet 4th grade.
