For every question, four probable answers bear in letters (A), (B), (C) and (D) are given. Only one out of these is correct. You have to choose the correct answer.
The least number which is divisible by 12, 15 and 25 is

Options

A. 300
B. 150
C. 200
D. 400

Answer

To find the least number that is divisible by 12, 15, and 25, we need to calculate the Least Common Multiple (LCM) of these three numbers. We will use the prime factorization method for this.

### Step-by-Step Solution:

1. **Prime Factorization of Each Number**:
- **12**:
- 12 can be factored into prime numbers as follows:
- 12 = 2 × 6
- 6 = 2 × 3
- So, the prime factorization of 12 is: \( 2^2 \times 3^1 \)

- **15**:
- 15 can be factored into prime numbers as follows:
- 15 = 3 × 5
- So, the prime factorization of 15 is: \( 3^1 \times 5^1 \)

- **25**:
- 25 can be factored into prime numbers as follows:
- 25 = 5 × 5
- So, the prime factorization of 25 is: \( 5^2 \)

2. **Identify the Highest Powers of Each Prime Factor**:
- From the factorizations, we identify the highest powers of all prime factors involved:
- For prime number 2: The highest power is \( 2^2 \) from 12.
- For prime number 3: The highest power is \( 3^1 \) from both 12 and 15.
- For prime number 5: The highest power is \( 5^2 \) from 25.

3. **Calculate the LCM**:
- Now, we multiply these highest powers together to find the LCM:
\[ LCM = 2^2 \times 3^1 \times 5^2 \]
- Calculating this step-by-step:
- \( 2^2 = 4 \)
- \( 3^1 = 3 \)
- \( 5^2 = 25 \)
- Now, multiply these together:
- \( 4 \times 3 = 12 \)
- \( 12 \times 25 = 300 \)

4. **Conclusion**:
- Therefore, the least number which is divisible by 12, 15, and 25 is **300**.

### Final Answer:
The least number which is divisible by 12, 15, and 25 is **300**.

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