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

Why do we want to take lcm? Please explain.

Commense is nothing but start tolling. here six bells are there and toll together at intervals 2,4,6,8,10,12

first bell tolls at every :2secs,4secs,6sec......120sec....

second bell tolls at every :4secs,8secs,12secs.....120secs.....

third bell tolls together at every:6sec,12sec,18sec..120sec...

fourth bell tolls together at every:8sec,16sec,24sec...120sec..

fifth bell tolls together at every:10sec,20sec,30sec ,....120sec...

sixth ell tolls together at every:12sec,24sec,36sec....120sec...

NOW OBSERVE ALL TOLLS the common sec in *All* bell tolls is 120sec

thats why we need to find l.c.m in shortcut
come to question:
1 toll altogether takes time=120sec
? tolls altogether takes time=1800sec(30min*60sec)

The number of tolls are 1800*1/120 = 15 tolls(times)


But in question:
Six bells commence tolling together(first toll) and also toll at intervals of 2, 4, 6, 8 10 and 12 beginning itself started from tollinf so we should consider that toll also.

Hence answer is 15 Tolls + First Toll == 16 dat's it.

Hope you understand.

Why take LCM? Please explain to me.

Thanks everyone for explaining.

@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.

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

@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.

Thank you @Sarvan.

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.

If two bells toll after every 3 secs and 4 secs respectively and if they commence tolling at the same time.

Then the first bell tolls after every 3, 6, 9, 12 secs...
The second bell tolls after every 4, 8, 12, ....
So they toll together again after 12 secs, which is the LCM

Henceforth they toll after every 12 seconds, i.e whenever the time is a common multiple of both 3 and 4.

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