Aptitude - Problems on H.C.F and L.C.M - Discussion

Because of all bells ring/toll together after every 2 min (120 s). So to find that how many times all bells tolled together in 30 mins we need to divide the episode i.e. 30 mins by 2 min (120 s).

At last, we add 1 because we have to count all the number of times the bells tolled together in 30 mins, as they started tolling together so their first toll also needs to be counted and hence we add 1 in 15 and get the answer as 16.

Can anyone please say it Ring or Start ringing?

In 30th min they meet together but they don't toil together. So it should be 15 not 16.

It shouldn't be +1 it is 2 that's when we get 16 as the answer.

Can you please tell me how to calculate LCM? I am not understanding.

@All.

Here, we should count 0 but 0 is the 60th second of the previous minute if we count this 0 it would be 30 minutes 1 second.

So please give me the correct solution.

I got the easiest way to understand the solution that how the answer is 16.

Look at your clock it starts from 12:00 and ends at 12:00.
Now consider each hour of your clock as a minute that means 12 to 1=1 min and 1 to 2=2min. So for 2min it's 12 to 2 = 2min.

Now starting from 12:00 start counting for 2 minutes interval taking 12:00 as 1(times the ring bell together).

So, 12:00 - 1
12:00 to 2:00 - 2 (2nd time they rang together)
2:00 to 4:00 - 3
.
.
.
.
.
10:00 to 12:00 - 7 and now you have completed your 12 minutes out of 30 minutes.

Repeat the same process you will complete 24 minutes out of your 30 minutes and 13 times the bell rang together.

Now you are left with 6 minutes.
so 12:00 - 2:00 = 14 times.
2:00 - 4:00 = 15 times.
4:00 - 6:00 = 16 times.

Finally, you have completed your 30 minutes and the bell rang 16 times.

Hope now you people could understand how the answer is 16.

Thanks @Balaraju Hari.

I cannot understand why 1 is added in the last step?

We know that 1st bell will commence on 0 min. Then in 30 min, 15 other bells will be tolling at every 2 min. Of interval. Therefore if we add all of these. Answer will be 15 + 1=16.