42 Uniform Oscillator are One bell 421 hurch bells The bells

4.2 Uniform Oscillator are One bell 4.2.1 hurch bells The bells of two different churches ringing. the bells rings every 3 seconds, and the other rings every 4 seconds. Assume that they ring have just rung at the same time. How long will it be until the next time using the together? Answer the question in two ways: using common sense, and method of Example 4.2.1.

Solution

The first bell rings after every 3 secs and second bell rings after every 4 secs. They have just rung together at the same time.

Then the first bell rings after every 3, 6, 9, 12 secs.... and
The second bell rings after every 4, 8, 12, .....
So, they will ring together again after 12 secs, which is the LCM of (3, 4).

It implies they ring after every 12 seconds, i.e whenever the time is a common multiple of both 3 and 4.