Bell Problem

A first bell ring at every 6 minutes, a second bell rings every 7 minutes and a third bell rings every 1 hour, if all the bells start ringing at 12 noon today when the next day will all ring at the same time?

Solution

-The 1st two bells will ring at the same time every 6*7 = 42 mn

-The 3rd bell ring once every hour, or once every 60mn

-What is the smallest multiple of 42 that is evenly divided by 60?

(10*42)/60 = 420/60 =7

-So, every 420 min, all 3 bells ring together

420/60 = 7h

-12 noon : 12pm + 7h = 7pm is when they all ring together