Find the least common multiple (LCM) for each set of three numbers on this educational worksheet.

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: \(9, 27, 2\)

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

2. Identify the Highest Powers:
- 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: \(14, 17, 12\)

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

2. Identify the Highest Powers:
- 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: \(19, 14, 8\)

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

2. Identify the Highest Powers:
- 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: \(24, 11, 14\)

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

2. Identify the Highest Powers:
- 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: \(3, 10, 14\)

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

2. Identify the Highest Powers:
- 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: \(14, 28, 21\)

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

2. Identify the Highest Powers:
- 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: \(9, 13, 26\)

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

2. Identify the Highest Powers:
- 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: \(13, 29, 21\)

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

2. Identify the Highest Powers:
- 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: \(18, 29, 21\)

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

2. Identify the Highest Powers:
- 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:
\[
\text{LCM} = 2^1 \times 3^2 \times 7^1 \times 29^1 = 2 \times 9 \times 7 \times 29 = 3726
\]

Answer: \(\boxed{3726}\)

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Problem 10: \(27, 23, 15\)

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

2. Identify the Highest Powers:
- 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:

\[
\boxed{54, 1428, 1064, 1848, 210, 84, 234, 7833, 3726, 3105}
\]