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

Options

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

Answer

To find the Least Common Multiple (LCM) of the numbers 12, 15, 20, and 25, we can use the method of prime factorization. Here’s a step-by-step solution:

### Step 1: 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 of Each Prime Factor
Now, we will take the highest power of each prime factor from 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: Calculate the LCM
Now, we multiply these highest powers together to get 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:
\[ \text{LCM} = 4 \times 3 \times 25 \]

Calculating further:
- \(4 \times 3 = 12\)
- \(12 \times 25 = 300\)

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

---