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

Can you tel me how is the HCM can find? Explain with any example.

Actually got solution.

All bells starting from 1 second at a time 1 time bells tolling at a time.

1st bell tolling every 2 sec means 2, 4, 6, 8,...120...240... 360....480

2nd bell tolling every 4 sec means 4, 8, 12, 16...120...240...360...480

3rd bell tolling every 6 sec means 6, 12, 18, 24...120...240...360...480

4th bell tolling every 8 sec means 8, 16, 24...120...240...360...480

5th bell tolling every 10 sec means 10, 20, 30...120...240...360...480

6th bell tolling every 6 sec means 12, 24, 36...120...240...360...480

So 1 sec =1 time tolling at a time.

120 sec = 2 time tolling at a time.

240 sec = 3 time tolling at a time.

360 sec = 4 time tolling at a time.

4800 sec = 5 time tolling.

600 sec = 6 time tolling at a time.
.
.
Last 1800 sec = 16 time tolling at a time.

Total time bells tolling at a time =16 times.

Why not using HCM:

Suppose 3 bells are tolling at 2, 4, 6 sec,

HCM is 2, so now think, is it possible that they will toll at every 2 sec. NO.

We will have to find a common number (multiple) which is occurring to every bell and that is called LCM.

So LCM here is 12.

That means every bell will toll at 12th second.

I am unable to understand why we are using lcm method for this problem. Can anyone explain?

Why we find the L.C.M.?

I can't understand the L.C.M. method. What is the difference between L.C.M and H.C.M. Why didn't use the H.C.M. method in here. Please anyone can explain me.

Well, I will break it into English but no maths.

Generally all the bells rang (toll) at its first encounter, that means all 6 bells started its journey by joining all their hands at once, i.e., at 0th sec<< remember this started journey>>.

Then they lost their hands and joined again at 120th second, in the mean-while they are tolling individually and not combinedly.

1. It is nothing but at 14th 19th. 25th 38th 57th 69th. Until 119th sec they didn't rang combinedly then at *120th* sec they combined their hands and rung. This is the least number that those 6 bells have waited for their combined toll (nothing but LCM in maths criteria), shortcut used.

2. Then they again rung combinedly after *120*+120th=240th sec+. 120+120+..until 1800.

3. They had given us 30min =1800 sec) , so if we divide that 1800 sec by 120sec (intervals) 1800/120=15 we will get.

Actually this (15) should be the answer if all the bells did not start combinedly, but our bad luck, they mentioned in the question that ""Six bells commence tolling together. "" that means they have started its journey itself by ringing combinedly.

4. The extra +1 is nothing but this started journey.

Now go through what @Saravan and all others said you will get more detailed idea.

Hope this understands. Thank you.

Why 30 is divide by 2, please explain?

It's asked in the question that Six bells commence tolling together and toll at intervals of 2, 4, 6, 8 10 and 12 seconds respectively. In 30 minutes, how many times do they toll together?

Here as per the question the 1st bell can toll 15 times in 30 min i.e (30/2), 2nd bell can toll 7.5 times in 30 min i.e 30/4, 3rd bell 5 times, 4th bell 3.7 times, 5th bell 3 times and 6th one 2.5 times in 30 min...together they tolled 36.7 times in 30 min..

Why this approach is wrong?

Since the bells start tolling together, the first toll also needs to be counted. Therefore we need to add 1.

Why at last 1 has been added?