Five bells ring together at the intervals of 3,5,8,9 and 10 seconds. All the bells ring simultaneously at the same time. They will again ring simultaneously after :

Options

A. 6 min
B. 8 min
C. 9 min
D. 4 min

Answer

To find out when the five bells will ring together again, we need to calculate the Least Common Multiple (LCM) of their ringing intervals: 3, 5, 8, 9, and 10 seconds.

### Step-by-Step Solution:

1. **List the intervals**: The ringing intervals of the bells are 3, 5, 8, 9, and 10 seconds.

2. **Find the prime factorization of each interval**:
- 3 = 3^1
- 5 = 5^1
- 8 = 2^3
- 9 = 3^2
- 10 = 2^1 × 5^1

3. **Identify the highest power of each prime factor**:
- For the prime number 2: The highest power is 2^3 (from 8).
- For the prime number 3: The highest power is 3^2 (from 9).
- For the prime number 5: The highest power is 5^1 (from 5 and 10).

4. **Multiply the highest powers together**:
- LCM = 2^3 × 3^2 × 5^1
- LCM = 8 × 9 × 5

5. **Calculate the product step-by-step**:
- First, calculate 8 × 9 = 72.
- Then, calculate 72 × 5 = 360.

6. **Conclusion**: The bells will ring together again after 360 seconds.

### Final Answer:
The five bells will ring simultaneously again after **360 seconds**.

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