To determine when two bells ringing at intervals of 8 minutes and 12 minutes, respectively, will ring together again after starting simultaneously at 12:00 noon, we follow these steps:
1. Find the Least Common Multiple (LCM):
- The first bell rings every 8 minutes.
- The second bell rings every 12 minutes.
- The LCM of 8 and 12 is the smallest time interval at which both bells will ring together.
2. Calculate the LCM:
- The LCM of two numbers is the smallest number that is a multiple of both.
Knowing that the LCM of 8 and 12 is 24 minutes, we conclude that both bells will ring together every 24 minutes.
3. Determine the Exact Time they Ring Together:
- They start ringing together at 12:00 noon.
- Adding 24 minutes to 12:00 noon gives us the next time they will ring together.
4. Convert the Time:
- Starting from 12:00 noon, we add 24 minutes:
- 12:00 PM + 24 minutes = 12:24 PM
### Solution:
- The two bells will ring together every 24 minutes.
- The first time they ring together after starting at 12:00 noon is at 12:24 PM.
So, the bells will ring together again at 12:24 PM.
