Answer:
60 times will they ring together at the same second in one hour excluding the one at the end.
Step-by-step explanation:
Given : Five bells begin to ring together and they ring at intervals of 3, 6, 10, 12 and 15 seconds, respectively.
To find : How many times will they ring together at the same second in one hour excluding the one at the end?
Solution : 
First we find the LCM of 3, 6, 10, 12 and 15.
2 | 3  6  10  12  15
2 | 3  3   5   6  15
3 | 3  3   5   3  15
5 | 1    1  5   1    5
   | 1    1   1   1     1


So, the bells will ring together after every 60 seconds i.e. 1 minutes.
i.e. in 1 minute they rand together 1 time.
We know, 1 hour = 60 minutes
So, in 60 minute they rang together 60 times.
Therefore, 60 times will they ring together at the same second in one hour excluding the one at the end.