Four bells toll together at 9:00a.m. They toll after 7,8,11 and 12 seconds respectively. How many times will they toll together again in the next three times?

To determine when the four bells will toll together again, we need to find the least common multiple (LCM) of their respective tolling intervals. Let's calculate the LCM for the given intervals: 7, 8, 11, and 12 seconds.

The prime factors of these numbers are:
7 = 7
8 = 2^3
11 = 11
12 = 2^2 * 3

The LCM is the product of the highest powers of all prime factors:
LCM = 2^3 * 3 * 7 * 11 = 2 * 2 * 2 * 3 * 7 * 11 = 8 * 3 * 77 = 1848

Therefore, the four bells will toll together again every 1848 seconds.

Now, let's find out how many times they will toll together in the next three intervals of time.

Next interval:
There are 60 seconds in a minute, so the next interval is 60 seconds after 9:00 a.m., which is 9:01 a.m. or 01:00:00.
In this interval, there are 3600 seconds.
Number of tolls = 3600 / 1848 = 1.95

However, we are interested in the number of times they toll together, which is an integer value. Therefore, in the next interval, they will toll together 1 time.

Following interval:
The next interval is 60 seconds after 01:00:00, which is 01:01:00.
Again, there are 3600 seconds in this interval.
Number of tolls = 3600 / 1848 = 1.95

They will toll together 1 time in this interval as well.

Third interval:
The third interval is 60 seconds after 01:01:00, which is 01:02:00.
Once more, there are 3600 seconds in this interval.
Number of tolls = 3600 / 1848 = 1.95

They will toll together 1 time in this interval too.

In summary, they will toll together 1 time in each of the next three intervals of 60 seconds.