Least Common Multiple Worksheets | Download Free Printables For Kids - Free Printable

To find the Least Common Multiple (LCM) of three numbers, we need to determine the smallest number that is a multiple of all three given numbers. The LCM can be found using the prime factorization method or by identifying the highest powers of all prime factors present in the numbers.

Let's solve each problem step by step:

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Problem 1: Find the LCM of 9, 27, and 2

1. Prime Factorization:
- \( 9 = 3^2 \)
- \( 27 = 3^3 \)
- \( 2 = 2^1 \)

2. Identify the Highest Powers of All Prime Factors:
- For \( 3 \): The highest power is \( 3^3 \) (from 27).
- For \( 2 \): The highest power is \( 2^1 \) (from 2).

3. Calculate the LCM:
\[
\text{LCM} = 3^3 \times 2^1 = 27 \times 2 = 54
\]

Answer: \( \boxed{54} \)

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Problem 2: Find the LCM of 14, 17, and 12

1. Prime Factorization:
- \( 14 = 2 \times 7 \)
- \( 17 = 17 \) (prime)
- \( 12 = 2^2 \times 3 \)

2. Identify the Highest Powers of All Prime Factors:
- For \( 2 \): The highest power is \( 2^2 \) (from 12).
- For \( 3 \): The highest power is \( 3^1 \) (from 12).
- For \( 7 \): The highest power is \( 7^1 \) (from 14).
- For \( 17 \): The highest power is \( 17^1 \) (from 17).

3. Calculate the LCM:
\[
\text{LCM} = 2^2 \times 3^1 \times 7^1 \times 17^1 = 4 \times 3 \times 7 \times 17 = 1428
\]

Answer: \( \boxed{1428} \)

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Problem 3: Find the LCM of 19, 14, and 8

1. Prime Factorization:
- \( 19 = 19 \) (prime)
- \( 14 = 2 \times 7 \)
- \( 8 = 2^3 \)

2. Identify the Highest Powers of All Prime Factors:
- For \( 2 \): The highest power is \( 2^3 \) (from 8).
- For \( 7 \): The highest power is \( 7^1 \) (from 14).
- For \( 19 \): The highest power is \( 19^1 \) (from 19).

3. Calculate the LCM:
\[
\text{LCM} = 2^3 \times 7^1 \times 19^1 = 8 \times 7 \times 19 = 1064
\]

Answer: \( \boxed{1064} \)

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Problem 4: Find the LCM of 24, 11, and 14

1. Prime Factorization:
- \( 24 = 2^3 \times 3 \)
- \( 11 = 11 \) (prime)
- \( 14 = 2 \times 7 \)

2. Identify the Highest Powers of All Prime Factors:
- For \( 2 \): The highest power is \( 2^3 \) (from 24).
- For \( 3 \): The highest power is \( 3^1 \) (from 24).
- For \( 7 \): The highest power is \( 7^1 \) (from 14).
- For \( 11 \): The highest power is \( 11^1 \) (from 11).

3. Calculate the LCM:
\[
\text{LCM} = 2^3 \times 3^1 \times 7^1 \times 11^1 = 8 \times 3 \times 7 \times 11 = 1848
\]

Answer: \( \boxed{1848} \)

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Problem 5: Find the LCM of 3, 10, and 14

1. Prime Factorization:
- \( 3 = 3 \)
- \( 10 = 2 \times 5 \)
- \( 14 = 2 \times 7 \)

2. Identify the Highest Powers of All Prime Factors:
- For \( 2 \): The highest power is \( 2^1 \) (from 10 and 14).
- For \( 3 \): The highest power is \( 3^1 \) (from 3).
- For \( 5 \): The highest power is \( 5^1 \) (from 10).
- For \( 7 \): The highest power is \( 7^1 \) (from 14).

3. Calculate the LCM:
\[
\text{LCM} = 2^1 \times 3^1 \times 5^1 \times 7^1 = 2 \times 3 \times 5 \times 7 = 210
\]

Answer: \( \boxed{210} \)

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Problem 6: Find the LCM of 14, 28, and 21

1. Prime Factorization:
- \( 14 = 2 \times 7 \)
- \( 28 = 2^2 \times 7 \)
- \( 21 = 3 \times 7 \)

2. Identify the Highest Powers of All Prime Factors:
- For \( 2 \): The highest power is \( 2^2 \) (from 28).
- For \( 3 \): The highest power is \( 3^1 \) (from 21).
- For \( 7 \): The highest power is \( 7^1 \) (from all three numbers).

3. Calculate the LCM:
\[
\text{LCM} = 2^2 \times 3^1 \times 7^1 = 4 \times 3 \times 7 = 84
\]

Answer: \( \boxed{84} \)

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Problem 7: Find the LCM of 9, 13, and 26

1. Prime Factorization:
- \( 9 = 3^2 \)
- \( 13 = 13 \) (prime)
- \( 26 = 2 \times 13 \)

2. Identify the Highest Powers of All Prime Factors:
- For \( 2 \): The highest power is \( 2^1 \) (from 26).
- For \( 3 \): The highest power is \( 3^2 \) (from 9).
- For \( 13 \): The highest power is \( 13^1 \) (from 13 and 26).

3. Calculate the LCM:
\[
\text{LCM} = 2^1 \times 3^2 \times 13^1 = 2 \times 9 \times 13 = 234
\]

Answer: \( \boxed{234} \)

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Problem 8: Find the LCM of 13, 29, and 21

1. Prime Factorization:
- \( 13 = 13 \) (prime)
- \( 29 = 29 \) (prime)
- \( 21 = 3 \times 7 \)

2. Identify the Highest Powers of All Prime Factors:
- For \( 3 \): The highest power is \( 3^1 \) (from 21).
- For \( 7 \): The highest power is \( 7^1 \) (from 21).
- For \( 13 \): The highest power is \( 13^1 \) (from 13).
- For \( 29 \): The highest power is \( 29^1 \) (from 29).

3. Calculate the LCM:
\[
\text{LCM} = 3^1 \times 7^1 \times 13^1 \times 29^1 = 3 \times 7 \times 13 \times 29 = 7833
\]

Answer: \( \boxed{7833} \)

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Problem 9: Find the LCM of 18, 29, and 21

1. Prime Factorization:
- \( 18 = 2 \times 3^2 \)
- \( 29 = 29 \) (prime)
- \( 21 = 3 \times 7 \)

2. Identify the Highest Powers of All Prime Factors:
- For \( 2 \): The highest power is \( 2^1 \) (from 18).
- For \( 3 \): The highest power is \( 3^2 \) (from 18).
- For \( 7 \): The highest power is \( 7^1 \) (from 21).
- For \( 29 \): The highest power is \( 29^1 \) (from 29).

3. Calculate the LCM:
\[
\text{LCM} = 2^1 \times 3^2 \times 7^1 \times 29^1 = 2 \times 9 \times 7 \times 29 = 3654
\]

Answer: \( \boxed{3654} \)

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Problem 10: Find the LCM of 27, 23, and 15

1. Prime Factorization:
- \( 27 = 3^3 \)
- \( 23 = 23 \) (prime)
- \( 15 = 3 \times 5 \)

2. Identify the Highest Powers of All Prime Factors:
- For \( 3 \): The highest power is \( 3^3 \) (from 27).
- For \( 5 \): The highest power is \( 5^1 \) (from 15).
- For \( 23 \): The highest power is \( 23^1 \) (from 23).

3. Calculate the LCM:
\[
\text{LCM} = 3^3 \times 5^1 \times 23^1 = 27 \times 5 \times 23 = 3105
\]

Answer: \( \boxed{3105} \)

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Final Answers:

\[
\boxed{54, 1428, 1064, 1848, 210, 84, 234, 7833, 3654, 3105}
\]