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

@Kyra.

Here, it is asked in 30 minutes how many times 6 ring balls roll together.

6 ring balls roll every 2 minutes
So, we divided for 30 minutes how many 2-interval exist.

HCF is 2
Then 30/2 = 15
Stating stage 1time ,15 + 1 = 16.

@Sathyaraj.

In this case, for every 120 seconds, all six bells ring together.
Let us look in another perspective.
At 120th second,
The first bell would have ringed for 60 times.
The second bell would have ringed for 30 times.
The third bell would have ringed for 20 times.
The fourth bell would have ringed for 15 times.
The fifth bell would have ringed for 12 times.
The sixth bell would have ringed for 10 times.

Here, the point is that even though these bells are ringed several times only at the 120th second all of these six bells ring simultaneously.
Only for this purpose the LCM is used in this problem.

Why take LCM? Please explain to me.

Thanks for the answer.

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.

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

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

Why did we add 1? Please tell me.