Question

There are four bells, which ring at intervals of 3,7,12 and 14 respectively. The four bells begin to ring at 12 o'clock. When will they next ring together?

PLEASE EXPLAIN ​

Answer 1

Answer:

The four bells will next toll together after 1 minute 24 second.

Step-by-step explanation:

Given, there are four bells which toll at intervals of 3, 7, 12, and 14 seconds respectively.

The four bells begin to toll at 12 o' clock.

We need to find when will they next toll together.

For that, we have find the L.C.M of all time intervals.

Finding L.C.M of 3, 7, 12, 14

write numbers as multiplication of its prime factors

3 → 3 comes once

7→ 7 comes once

12→ 2 ×3×2 → 2 comes twice and three comes once

14→ 2×7 → 2 comes once and 7 comes once

So the maximum is three comes once and 7 comes once and 2 comes twice

Hence least common multiple is 3×7×2×2 = 84

Now, 84 sec = 1 min 24 sec

the next toll together after 1 min 24 sec

hence, they will toll together at 12 : 01 : 24