Question

Find the least common multiple.
5 and 12

Answer 1

To find the least common multiple (LCM) of 5 and 12, we can use the prime factorization method or the formula involving the greatest common divisor (GCD).

First, we can identify the prime factors of each number:

- The prime factorization of 5 is \(5^1\).
- The prime factorization of 12 is \(2^2 \times 3^1\).

To find the LCM, we take the highest power of each prime that appears in either factorization:

- For the prime number 2, the highest power is \(2^2\) (from 12).
- For the prime number 3, the highest power is \(3^1\) (from 12).
- For the prime number 5, the highest power is \(5^1\) (from 5).

Now, we multiply these together to get the LCM:

\[
\text{LCM} = 2^2 \times 3^1 \times 5^1 = 4 \times 3 \times 5
\]

Calculating that step by step:

1. \(4 \times 3 = 12\)
2. \(12 \times 5 = 60\)

So, the least common multiple of 5 and 12 is \( \boxed{60} \).