Question

Four bells are ringing at intervals of $12,16,24$ and$36$ minutes. They start ringing simultaneously at $12$ o'clock. Find when will they again ring together? What is the LCM of the intervals of the ringing of the bells?

Answer 1

The LCM of 12, 16, 24 and 36 minutes will gives us the next time they will all ring together.

$12=2\times 2\times 3$

$16=2\times 2\times 2\times 2$

$24=2\times 2\times 2\times 3$

$36=2\times 2\times 3\times 3$
The LCM $=2\times 2\times 2\times 2\times 3\times 3=144$ minutes.
The time when the bells will ring simultaneously is $144$ minutes after $12:00pm$ or at $2:24pm$.