Bells of three churches toll at the interval of 10, 12 and 15 minutes, respectively. If they start to toll together at 8.30 a.m., when will they toll together again?

Options

A. 9.00 a.m.
B. 9.30 a.m.
C. 10.00 a.m.
D. 12.00 noon

Answer

To solve the problem of when the bells of three churches will toll together again after starting at 8:30 a.m., we need to find the least common multiple (LCM) of the intervals at which the bells toll. The intervals are 10 minutes, 12 minutes, and 15 minutes.

### Step-by-Step Solution:

1. **Identify the intervals**:
- Bell 1 tolls every 10 minutes.
- Bell 2 tolls every 12 minutes.
- Bell 3 tolls every 15 minutes.

2. **Find the LCM of the intervals**:
- To find the LCM, we can list the multiples of each interval until we find a common multiple.

- **Multiples of 10**: 10, 20, 30, 40, 50, 60, 70, ...
- **Multiples of 12**: 12, 24, 36, 48, 60, 72, ...
- **Multiples of 15**: 15, 30, 45, 60, 75, ...

The smallest common multiple in all three lists is **60**.

3. **Interpret the LCM**:
- The LCM of 10, 12, and 15 is 60 minutes. This means that the bells will toll together again after 60 minutes.

4. **Calculate the time when they will toll together again**:
- Starting time: 8:30 a.m.
- Add 60 minutes (1 hour) to 8:30 a.m.
- 8:30 a.m. + 1 hour = 9:30 a.m.

### Final Answer:
The bells will toll together again at **9:30 a.m.**.