Question

Five bells begin to ring together and they ring at intervals of 3, 6, 10, 12 and 15 seconds, respectively. How many times will they ring together at the same second in one hour excluding the one at the end?

Answer 1

60 times will they ring together at the same second in one hour excluding the one at the end.

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

`LCM(3, 6, 10, 12,15)=2* 2* 3* 5`

`LCM(3, 6, 10, 12,15)=60`

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.