Lcm online exercise - Free Printable

To solve the problem of finding the Least Common Multiple (LCM) using the factor tree method, we need to break down each number into its prime factors and then determine the LCM based on those factors. Let's go through the steps for each pair of numbers.

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Step 1: Factor Tree for 21 and 14

#### Factor Tree for 21:
- Start with 21.
- Break it down into its prime factors:
- \( 21 = 3 \times 7 \)
- So, the prime factors of 21 are \( 3 \) and \( 7 \).

#### Factor Tree for 14:
- Start with 14.
- Break it down into its prime factors:
- \( 14 = 2 \times 7 \)
- So, the prime factors of 14 are \( 2 \) and \( 7 \).

#### Finding the LCM:
- List all the prime factors from both numbers, taking the highest power of each prime that appears:
- From 21: \( 3^1 \) and \( 7^1 \)
- From 14: \( 2^1 \) and \( 7^1 \)
- The LCM is the product of these highest powers:
- \( \text{LCM} = 2^1 \times 3^1 \times 7^1 = 2 \times 3 \times 7 = 42 \)

#### Answer for 21 and 14:
\[ \text{LCM} = 2 \times 3 \times 7 = 42 \]

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Step 2: Factor Tree for 55 and 22

#### Factor Tree for 55:
- Start with 55.
- Break it down into its prime factors:
- \( 55 = 5 \times 11 \)
- So, the prime factors of 55 are \( 5 \) and \( 11 \).

#### Factor Tree for 22:
- Start with 22.
- Break it down into its prime factors:
- \( 22 = 2 \times 11 \)
- So, the prime factors of 22 are \( 2 \) and \( 11 \).

#### Finding the LCM:
- List all the prime factors from both numbers, taking the highest power of each prime that appears:
- From 55: \( 5^1 \) and \( 11^1 \)
- From 22: \( 2^1 \) and \( 11^1 \)
- The LCM is the product of these highest powers:
- \( \text{LCM} = 2^1 \times 5^1 \times 11^1 = 2 \times 5 \times 11 = 110 \)

#### Answer for 55 and 22:
\[ \text{LCM} = 2 \times 5 \times 11 = 110 \]

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Final Answers:

1. For 21 and 14:
\[
\boxed{2 \times 3 \times 7 = 42}
\]

2. For 55 and 22:
\[
\boxed{2 \times 5 \times 11 = 110}
\]