Find the LCM of 12, 15, 20 and 25.

Options

A. 100
B. 150
C. 300
D. 400

Answer

To find the LCM (Least Common Multiple) of the numbers 12, 15, 20, and 25, we can follow these steps:

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

- **12**:
- 12 = 2 × 2 × 3 = \(2^2 \times 3^1\)

- **15**:
- 15 = 3 × 5 = \(3^1 \times 5^1\)

- **20**:
- 20 = 2 × 2 × 5 = \(2^2 \times 5^1\)

- **25**:
- 25 = 5 × 5 = \(5^2\)

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

- For **2**: The highest power is \(2^2\) (from 12 and 20).
- For **3**: The highest power is \(3^1\) (from 12 and 15).
- For **5**: The highest power is \(5^2\) (from 25).

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

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

Calculating this step-by-step:

- \(2^2 = 4\)
- \(3^1 = 3\)
- \(5^2 = 25\)

Now, multiply these results:

\[ 4 \times 3 = 12 \]
\[ 12 \times 25 = 300 \]

### Conclusion
Thus, the LCM of 12, 15, 20, and 25 is **300**.

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