Question

Six different bells in a tower toll at the
intervals of 9 sec, 12 sec, 15 sec, 18 sec,
21 sec and 24 sec respectively. If all of
them toll at 6 am, the next time they toll
together is

Answer 1

SOLUTION

GIVEN

• Six different bells in a tower toll at the intervals of 9 sec, 12 sec, 15 sec, 18 sec, 21 sec and 24 sec respectively.

• All of them toll at 6 am

TO DETERMINE

The next time they toll together

EVALUATION

Here it is given that Six different bells in a tower toll at the intervals of 9 sec, 12 sec, 15 sec, 18 sec, 21 sec and 24 sec respectively.

Now we have to find the LCM of 9, 12, 15, 18, 21, 24 in order to determine the next time when they toll together

$9 = 3 \times 3$

$12 = 2 \times 2 \times 3$

$15 = 3 \times 5$

$18 = 2 \times 3 \times 3$

$21 = 3 \times 7$

$24 = 2 \times 2 \times 2 \times 3$

Hence the LCM of 9, 12, 15, 18, 21, 24

$\sf{ = 2 \times 2 \times 2 \times 3 \times 3 \times 5 \times 7}$

$= 2520$

Now 2520 second = 42 min

So the all bells in the tower toll is 42 min later 6 am

Hence the all bells in the tower toll at

6.42 am

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