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:
- \(4 \times 3 = 12\)
- \(12 \times 5 = 60\)
So, the least common multiple of 5 and 12 is \( \boxed{60} \).