Question

three Bells toll at intervals of 12 18 20 minutes respectively if they start tolling together after what time will they next toll together

Answer 1

we need to find LCM(12,18,20)

$12 = {2}^{2} \times 3 \\ 18 = 2 \times {3}^{2} \\ 20 = {2}^{2} \times 5$
$lcm = {2}^{2} \times {3}^{2} \times 5 = 180$
all three bell will rang together after 180 min or 3 hours

Answer 2

They will ring together after 3 hours

GIVEN

Three Bells toll at intervals of 12 18 20 minutes respectively.

TO FIND

what time will they next toll together.

SOLUTION

We can simply solve the above problem as follows;

It is given that,

3 bells toll at intervals of 12 18 20 minutes respectively.

The time after which the three belles will ring together will be equal to the LCM of 12,18 and 20.

LCM of 12,18, and 20

2 |12, 18, 20

2|6, 9, 10

3 |3, 9, 5

3 |1, 3, 5

5| 1, 1, 5

| |1,1,1

LCM = 2×2×3×3×5 = 180

They will ring after 180 minutes

We can 180 minutes in hours as 180/60 = 3 hours

Hence, They will ring together after 3 hours

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