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

One is add because it is clearly given in the question that.

"Six bells commence tolling together" that means all bells rang once than after that rang in intervals of 2 4 6 8 10 and 12.

So add 1 to answer.

Assuming the tolling follows Arithmetic Progression (AP).
2s, 4s, 6s, 8s, 10s, 12s.
a = 2 and d = 2
In 30 minutes i.e 1800s
Tn = 1800, n = ?
1800 = 2 + (n - 1) 2 = 2 ( 1 + n - 1)
1800 = 2n

n (minutes) = 900s ~ 15 (minutes)

n = 15 times
But note that the six bells started tolling together. Then, plus the first tolling, the number of times they will tolling together in 30 minutes is 16 times

ANSWER = 16 times

@ Neem.
To find the LCM of 2,4,6,8,10, and 12 using Rasabtol Cross Method (RCM).

2 x 4 x 6 x 8 x 10 x 12 = 2 [1 x 2 x 3 x 4 x 5 x 6]

2 [1 x 3 x 5 x {2 ( 1 x 2 x 3)}]

Apply BODMAS rule,

= 2 [1 x3 x 5 x 2 x 6]

= 2 [1 x 2 x 5 x 3 (1x2)]

= 2 [1 x 2 x 5 x 3 (2)]

= 2 [60]

= 120.
Hence, the LCM = 120

LCM method
2 sec, 4 sec, 6 sec, 8 sec, 10 sec, 12 sec = all number is divisible by 2
i.e 1,2,3,4,5,6
= 1x2x3x4x5x6=720
=720/6(bells) = 120 seconds i.e 120/60(seconds) =2 minutes

In 30 minutes, they will toll together = 30/2=15

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

Therefore 15+1=16.

30/2 in order to calculate time for in fractions to each minute, as the LCM gave 2 minutes as the time.

Superb, it is indispensable for general competition.

Why at last 1 has been added?

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

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?

Why 30 is divide by 2, please explain?