Question

Three bells commence ringing together and ring at intervals of 2,4 and 12 seconds respectively.In 30 minutes, how many times do they ring together?

Answer 1

The least common multiple (LCM) of 2, 4 and 12 is 12. Thus, the bells toll together every 12 seconds, so in 30 minutes or 1800s they will toll simultaneously 1800/12 = 150 times. However, since they commence tolling together at the beginning (i.e., they are tolling together at the 0th second or the 0th minute), we need to add 1 to 150 and thus they toll together a total of 151 times.