Question

6 bells of a church toll at different intervals of 5seconds 8 seconds 10 seconds 6 seconds 12 seconds and 15 seconds respectively. if they toll together at 12 noon how many times will they toll together till 1 pm

Answer 1

There are six bells.

They toll at intervals of 5, 6, 8, 10, 12 & 15seconds.

Now

5 = 5

6 = 2 ×3

8 = 2 × 2 × 2

10 = 2 × 5

12 = 2 × 2 × 3

15 = 3 × 5

The least common multiple of 5,6,8,10,12 & 15 is 120

Hence the bells shall toll together after every 120 seconds

Now 120 s = 2 minutes

From 12 noon to 1pm there are 60 minutes

The bells toll together at every 2 minutes

Hence they shall toll together 60 /2 = 30 times from 12 noon to 1 pm