Find the LCM of 15, 25, and 125.

Options

A. 5
B. 125
C. 300
D. 375

Answer

To find the LCM (Least Common Multiple) of the numbers 15, 25, and 125, we can follow these steps:

### Step 1: Prime Factorization
First, we need to find the prime factorization of each number.

- **15** can be factored into primes as:
\[ 15 = 3 \times 5 \]

- **25** can be factored into primes as:
\[ 25 = 5^2 \]

- **125** can be factored into primes as:
\[ 125 = 5^3 \]

### Step 2: Identify the Highest Powers
Next, we will identify the highest power of each prime factor that appears in the factorizations.

- For the prime **3**, the highest power is \(3^1\) (from 15).
- For the prime **5**, the highest power is \(5^3\) (from 125).

### Step 3: Calculate the LCM
Now, we multiply these highest powers together to find the LCM.

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

Calculating this gives:

\[ \text{LCM} = 3 \times 125 = 375 \]

### Conclusion
Thus, the LCM of 15, 25, and 125 is:

\[ \text{LCM} = 375 \]