Question

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 will they toll together?
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Answer 1

Answer:

Hola Mate...

Now , Taking the LCM of 2,4,6,8, 10,12...

We get 120..

Now, We conclude that all bells will ring after 120 sec , or 2 mins......

In 30 mins they will roll together in

$\frac{30}{2}$

=15 and 1 at the starting.....

There fore , Total no. of bells together is 15 + 1 ==>>

16

Answer 2

Solution:-

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For example, let the two bells toll after every 3 and 4 seconds respectively.

Then the first bell tolls after every 3, 6, 9, 12 seconds...

Like this, the second bell tolls after every 4, 8, 12 seconds...

So, if the two bell toll together now, again they will toll together after 12 seconds. This 12 is the least common multiple (LCM) of 3 and 4.

The same thing happened in our problem. To find the time, when they will all toll together, we have to find the LCM of (2, 4, 8, 6, 10, 12).

LCM (2, 4, 8, 6, 10, 12) is 120

That is, 120 seconds or 2 minutes.

So, after every two minutes, all the bell will toll together.

For example, in 10 minutes, they toll together :

10/2  =  5 times

That is, after 2, 4, 6, 8, 10 minutes. It does not include the one at the start.

Similarly, in 30 minutes, they toll together :

=  30/2

=  15 times (excluding one at the start).

or 15+1=16times (including one at the start)

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