Upon calculating the LCM of the bells' tolling intervals, we find that the next tolling together would be at 1:00 AM the following day, but none of the given options reflect this. Therefore, there is an error in the provided choices.
To find when the four bells toll together again, we need to determine the least common multiple (LCM) of their tolling intervals: 12, 18, 20, and 25 minutes. The LCM of these numbers is 900 minutes, which is equivalent to 15 hours. If the bells first toll together at 10:00 AM, adding 15 hours brings us to 1:00 AM the next day. However, the choices given all fall within the same day. The problem as presented does not allow for a correct answer within the given options. Hence, we cannot choose options A, B, C, or D.
The LCM gives us the next time the bells will toll together after the starting point of 10:00 AM, showing the importance of understanding how to calculate multiples and apply them to real-world scenarios like this bell-tolling problem. In conclusion, without the correct option listed, we need to inform the student that there is likely an error in the problem or the choices provided.