Math worksheet for finding the least common multiple of three numbers.
Worksheet titled "Least Common Multiple of Three Numbers" with 10 problems asking to find the LCM of three numbers each.
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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 of a set of numbers is the smallest number that is a multiple of all the numbers in the set. Here's how we can approach each problem step by step:
---
- Prime Factorization:
- \(8 = 2^3\)
- \(17 = 17^1\) (17 is a prime number)
- \(2 = 2^1\)
- Identify the highest power of each prime factor:
- For \(2\): The highest power is \(2^3\) (from 8).
- For \(17\): The highest power is \(17^1\) (from 17).
- LCM Calculation:
\[
\text{LCM} = 2^3 \times 17^1 = 8 \times 17 = 136
\]
- Answer:
\[
\boxed{136}
\]
---
- Prime Factorization:
- \(22 = 2 \times 11\)
- \(8 = 2^3\)
- \(4 = 2^2\)
- Identify the highest power of each prime factor:
- For \(2\): The highest power is \(2^3\) (from 8).
- For \(11\): The highest power is \(11^1\) (from 22).
- 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 \(2^3\) (from 72).
- For \(3\): The highest power is \(3^2\) (from 36 and 72).
- LCM Calculation:
\[
\text{LCM} = 2^3 \times 3^2 = 8 \times 9 = 72
\]
- Answer:
\[
\boxed{72}
\]
---
- Prime Factorization:
- \(3 = 3^1\)
- \(37 = 37^1\) (37 is a prime number)
- \(15 = 3^1 \times 5^1\)
- Identify the highest power of each prime factor:
- For \(3\): The highest power is \(3^1\) (from 3 and 15).
- For \(5\): The highest power is \(5^1\) (from 15).
- For \(37\): The highest power is \(37^1\) (from 37).
- 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 \(2^2\) (from 4).
- For \(5\): The highest power is \(5^1\) (from 5 and 10).
- 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 \(2^1\) (from 18 and 90).
- For \(3\): The highest power is \(3^2\) (from 18, 45, and 90).
- For \(5\): The highest power is \(5^1\) (from 45 and 90).
- 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 \(2^1\) (from 42 and 34).
- For \(3\): The highest power is \(3^1\) (from 42 and 21).
- For \(7\): The highest power is \(7^1\) (from 42 and 21).
- For \(17\): The highest power is \(17^1\) (from 34).
- 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 \(2^3\) (from 40).
- For \(5\): The highest power is \(5^2\) (from 50).
- 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 \(2^3\) (from 56 and 8).
- For \(7\): The highest power is \(7^1\) (from 56 and 14).
- 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 \(2^2\) (from 12).
- For \(3\): The highest power is \(3^1\) (from 33, 12, and 3).
- For \(11\): The highest power is \(11^1\) (from 33).
- LCM Calculation:
\[
\text{LCM} = 2^2 \times 3^1 \times 11^1 = 4 \times 3 \times 11 = 132
\]
- Answer:
\[
\boxed{132}
\]
---
1. \(\boxed{136}\)
2. \(\boxed{88}\)
3. \(\boxed{72}\)
4. \(\boxed{555}\)
5. \(\boxed{20}\)
6. \(\boxed{90}\)
7. \(\boxed{714}\)
8. \(\boxed{200}\)
9. \(\boxed{56}\)
10. \(\boxed{132}\)
---
1. LCM(8, 17, 2)
- Prime Factorization:
- \(8 = 2^3\)
- \(17 = 17^1\) (17 is a prime number)
- \(2 = 2^1\)
- Identify the highest power of each prime factor:
- For \(2\): The highest power is \(2^3\) (from 8).
- For \(17\): The highest power is \(17^1\) (from 17).
- LCM Calculation:
\[
\text{LCM} = 2^3 \times 17^1 = 8 \times 17 = 136
\]
- Answer:
\[
\boxed{136}
\]
---
2. LCM(22, 8, 4)
- Prime Factorization:
- \(22 = 2 \times 11\)
- \(8 = 2^3\)
- \(4 = 2^2\)
- Identify the highest power of each prime factor:
- For \(2\): The highest power is \(2^3\) (from 8).
- For \(11\): The highest power is \(11^1\) (from 22).
- 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 \(2^3\) (from 72).
- For \(3\): The highest power is \(3^2\) (from 36 and 72).
- LCM Calculation:
\[
\text{LCM} = 2^3 \times 3^2 = 8 \times 9 = 72
\]
- Answer:
\[
\boxed{72}
\]
---
4. LCM(3, 37, 15)
- Prime Factorization:
- \(3 = 3^1\)
- \(37 = 37^1\) (37 is a prime number)
- \(15 = 3^1 \times 5^1\)
- Identify the highest power of each prime factor:
- For \(3\): The highest power is \(3^1\) (from 3 and 15).
- For \(5\): The highest power is \(5^1\) (from 15).
- For \(37\): The highest power is \(37^1\) (from 37).
- 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 \(2^2\) (from 4).
- For \(5\): The highest power is \(5^1\) (from 5 and 10).
- 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 \(2^1\) (from 18 and 90).
- For \(3\): The highest power is \(3^2\) (from 18, 45, and 90).
- For \(5\): The highest power is \(5^1\) (from 45 and 90).
- 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 \(2^1\) (from 42 and 34).
- For \(3\): The highest power is \(3^1\) (from 42 and 21).
- For \(7\): The highest power is \(7^1\) (from 42 and 21).
- For \(17\): The highest power is \(17^1\) (from 34).
- 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 \(2^3\) (from 40).
- For \(5\): The highest power is \(5^2\) (from 50).
- 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 \(2^3\) (from 56 and 8).
- For \(7\): The highest power is \(7^1\) (from 56 and 14).
- 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 \(2^2\) (from 12).
- For \(3\): The highest power is \(3^1\) (from 33, 12, and 3).
- For \(11\): The highest power is \(11^1\) (from 33).
- LCM Calculation:
\[
\text{LCM} = 2^2 \times 3^1 \times 11^1 = 4 \times 3 \times 11 = 132
\]
- Answer:
\[
\boxed{132}
\]
---
Final Answers:
1. \(\boxed{136}\)
2. \(\boxed{88}\)
3. \(\boxed{72}\)
4. \(\boxed{555}\)
5. \(\boxed{20}\)
6. \(\boxed{90}\)
7. \(\boxed{714}\)
8. \(\boxed{200}\)
9. \(\boxed{56}\)
10. \(\boxed{132}\)
Parent Tip: Review the logic above to help your child master the concept of least common multiple worksheet pdf.
