Six bells commence tolling together at 7:59 am. They toll at intervals of 3,6,9,12 and 15 seconds respectively. How many times will they toll together till 8:16 am? (excluding the toll at 7:59 am)

They toll at intervals of 3,6,9,12 and 15 seconds respectively.

So we need to take the LCM of 3,6,9,12 and 15.

LCM of 3,6,9,12 and 15 = $$2\times\ 2\times\ 3\times\ 3\times\ 5$$

= 180 seconds

We know that 1 minute = 60 seconds. So 3 minutes = 180 seconds.

It means that after every 3 minutes, these will toll together.

The first time it was at 7:59 am.

So after that these will toll together at 8:02 am, 8:05 am, 8:08 am, 8:11 am, 8:14 am, and 8:17 am.

Hence till 8:16 am, 6 times these will toll together.