Four bells rings after on interval 9,12,15,18 sec. In 36 min how many times will they ring together .

Answer

To solve the problem of how many times four bells will ring together in 36 minutes given their ringing intervals of 9, 12, 15, and 18 seconds, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the ringing intervals**: The bells ring at intervals of 9 seconds, 12 seconds, 15 seconds, and 18 seconds.

2. **Find the Least Common Multiple (LCM)**: To determine when all four bells will ring together, we need to find the LCM of the intervals.

3. **Factor each interval**:
- 9 = 3²
- 12 = 2² × 3
- 15 = 3 × 5
- 18 = 2 × 3²

4. **Determine the LCM**:
- For LCM, take the highest power of each prime factor:
- From 9: 3²
- From 12: 2²
- From 15: 5
- From 18: 2 and 3²
- Thus, LCM = 2² × 3² × 5 = 4 × 9 × 5 = 180 seconds.

5. **Convert LCM to minutes**: Since we need the time in minutes, we convert 180 seconds to minutes:
- 180 seconds ÷ 60 seconds/minute = 3 minutes.

6. **Calculate how many times they ring together in 36 minutes**:
- The first time they ring together is at 3 minutes.
- To find out how many times they ring together in 36 minutes, we divide:
- 36 minutes ÷ 3 minutes = 12.

### Final Answer:
The four bells will ring together **12 times** in 36 minutes.

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