Three bells, toll at interval of 36 sec, 40 sec and 48 sec respectively. They start ringing together at particular time. They next toll together after:

Options

A. 6 minutes
B. 12minutes
C. 18 minutes
D. 24 minutes

Answer

To find out when the three bells will toll together again, we need to calculate the least common multiple (LCM) of the intervals at which they toll: 36 seconds, 40 seconds, and 48 seconds.

### Step-by-Step Solution:

1. **Identify the intervals**: The bells toll at intervals of 36 seconds, 40 seconds, and 48 seconds.

2. **Find the prime factorization of each interval**:
- For 36:
- 36 = 2 × 18
- 18 = 2 × 9
- 9 = 3 × 3
- So, the prime factorization of 36 is \(2^2 \times 3^2\).
- For 40:
- 40 = 2 × 20
- 20 = 2 × 10
- 10 = 2 × 5
- So, the prime factorization of 40 is \(2^3 \times 5^1\).
- For 48:
- 48 = 2 × 24
- 24 = 2 × 12
- 12 = 2 × 6
- 6 = 2 × 3
- So, the prime factorization of 48 is \(2^4 \times 3^1\).

3. **Determine the highest power of each prime factor**:
- For 2: The highest power is \(2^4\) (from 48).
- For 3: The highest power is \(3^2\) (from 36).
- For 5: The highest power is \(5^1\) (from 40).

4. **Calculate the LCM**:
\[ \text{LCM} = 2^4 \times 3^2 \times 5^1 \]
- Calculate \(2^4 = 16\)
- Calculate \(3^2 = 9\)
- Calculate \(5^1 = 5\)
- Now multiply these together:
\[ \text{LCM} = 16 \times 9 \times 5 \]
- First, calculate \(16 \times 9 = 144\)
- Then, calculate \(144 \times 5 = 720\)

5. **Convert seconds to minutes**:
- Since 720 seconds is equal to \( \frac{720}{60} = 12\) minutes.

### Final Answer:
The three bells will toll together again after **12 minutes**.