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
[tex]LCM(3, 6, 10, 12,15)=2\times 2\times 3\times 5[/tex]
[tex]LCM(3, 6, 10, 12,15)=60[/tex]
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.
