Question

The least common multiple of 14 and 21 is

Answer 1

To find the least common multiple (LCM) of 14 and 21, we can use the prime factorization method.

First, let's find the prime factorization of each number:

- **14**: The prime factors of 14 are \(2 \times 7\).
- **21**: The prime factors of 21 are \(3 \times 7\).

Next, to find the LCM, we take the highest power of each prime that appears in the factorizations:

- From 14, we have \(2^1\) and \(7^1\).
- From 21, we have \(3^1\) and \(7^1\).

Now we take the highest powers:
- \(2^1\) (from 14)
- \(3^1\) (from 21)
- \(7^1\) (common to both)

Now, multiply these together to find the LCM:
\[
\text{LCM} = 2^1 \times 3^1 \times 7^1 = 2 \times 3 \times 7
\]

Calculating this step-by-step:
\[
2 \times 3 = 6
\]
\[
6 \times 7 = 42
\]

Therefore, the least common multiple of 14 and 21 is \( \boxed{42} \).