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

why did we divide 30 by 2? Please explain me.

First we took;

2,4,6,8,10 in L.C.M.
After that, we have 120 seconds
Here, it's said 30minutes,
So, 1min = 60second,,
2min = 120second,
So,
We divide 30÷2 = 15.
At Starting stage one time rang 15+1=16.

@All.

Because initially, it's starting at 0 sec.

A least common multiple of (2, 4, 6, 8, 10 and 12)

we can write 2 = 1 * 2

4 = 22

6 = 2 * 3

8 = 23

10 = 2* 5

12 = 22 *3.

A least common multiple of (2, 4, 6, 8, 10 and 12) = 23 * 3 * 5.

= 8 * 3 * 5
= 120 sec

Bells ring together after every 120 sec.

Required number of times in 30 minutes (30 *60 seconds ) = [(30 *60)/120]

= 15

But we have to add 1 because at starting all bells will be rung once a time after that the ring 15 times.

= 15 + 1.
=16 times.

The required number of times when they toll together is 16.

Thanks everyone for explaining.

At first min all bell will till together then 3 because of 129-sec diff than 5, 6, 7, 9, 11, . 29 so.

Total is 15, not 16.

Thank you @Sarvan.

Why do we want to take lcm? Please explain.

See why 1 added here means, it is mentioned in the question that "six bells tolling together and tolls " already tolled at starting and tolling after in intervals.

Hope you all understand.

@Raksha.

1 is added because they commence together consider that at 0 sec.

Which mean first tolling happened at 0 sec,
2nd@120th sec,
3@240th sec and last happed @1800th sec.