Question

Six bells commence tolling together and toll at intervals of 2,4,6,8,10,12 min. respectively. In 30 hours,how many times do they toll together. Please explain every step..

Answer 1

Given : 6 bells commence tolling together and toll at intervals of 2 , 4 , 6 , 8 , 10 , 12 minutes respectively.

To find least time after each bells rings together we find LCM of 2 , 4 , 6 , 8 , 10 , 12 , As :

2 = 2 × 1 ,

4 = 2 × 2

6 = 2 × 3

8 = 2 × 2 × 2

10 = 2 × 5

And

12 = 2 × 2 × 3

So,

LCM of 2 , 4 , 6 , 8 , 10 , 12 = 2 × 2 × 2 × 3 ×5 = 120 , So

After each 120 minutes or 2 hours ( we know 1 hour = 60 minutes ) all 6 bells rings together .

So,

In 30 hours they will rings 15 times . But they also rings together at starting .

Therefore,

Total number of times they will rings together = 15 + 1 = 16