Question

ind the least common multiple (LCM)15 of 6 and .

Answer 1

To find the least common multiple (LCM) of 6 and 15, you can follow these steps:

1. **List the prime factors:**
- The prime factorization of 6 is: \(2 \times 3\)
- The prime factorization of 15 is: \(3 \times 5\)

2. **Identify the highest power of each prime factor:**
- From the factorizations, we identify:
- The prime factor \(2\) appears in \(6\) (with a power of \(1\)).
- The prime factor \(3\) appears in both \(6\) and \(15\) (with a maximum power of \(1\)).
- The prime factor \(5\) appears in \(15\) (with a power of \(1\)).

3. **Multiply the highest powers of each prime factor:**
- LCM = \(2^1 \times 3^1 \times 5^1 = 2 \times 3 \times 5\)

4. **Calculate the LCM:**
- \(2 \times 3 = 6\)
- \(6 \times 5 = 30\)

Thus, the least common multiple (LCM) of 6 and 15 is **30**.