Question

Least common multiple of 50 15 6

Answer 1

To find the least common multiple (LCM) of the numbers 50, 15, and 6, we can follow these steps:

1. **Find the prime factorization of each number**:
- \( 50 = 2 \times 5^2 \)
- \( 15 = 3 \times 5 \)
- \( 6 = 2 \times 3 \)

2. **Identify the highest power of each prime factor present in any of the numbers**:
- For the prime number \( 2 \): the highest power is \( 2^1 \) (from 50 and 6).
- For the prime number \( 3 \): the highest power is \( 3^1 \) (from 15 and 6).
- For the prime number \( 5 \): the highest power is \( 5^2 \) (from 50).

3. **Multiply these highest powers together**:
\[
\text{LCM} = 2^1 \times 3^1 \times 5^2
\]

Calculating this step-by-step:
- \( 2^1 = 2 \)
- \( 3^1 = 3 \)
- \( 5^2 = 25 \)

Now, multiply these together:
\[
2 \times 3 = 6
\]
\[
6 \times 25 = 150
\]

Thus, the least common multiple of 50, 15, and 6 is \( \boxed{150} \).