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

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.

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.

Why did we add 1? Please tell me.

Six bells commence tolling together at intervals of 2, 4, 6, 8, 10, and 12 seconds respectively. In 30 minutes, they toll together 16 times.

The concept used is Least common multiplication. But we have to add 1 because at the start all bells will be rung once a time after they ring 15.

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

Six bells commence tolling together and toll at intervals of 2, 4, 6, 8 10 and 12 seconds respectively.

Here all the bells commence toll together i.e. they all rang at 0th second, and from then they rang 15 times. So, we added 15+1 = 16.

The reason we added 1 in the answer "Six bells commence tolling together".

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.

Why do we need to do lcm? Anyone please explain to me.

@All.

Because initially, it's starting at 0 sec.