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<pre>
Take the case of 10Hz and 12Hz

LCM of 10 and 12 is 60.

That means that if I count this way the multiples of 10

111111111122222222223333333333444444444455555555556
123456789012345678901234567890123456789012345678901234567890
          x         x         x        x         x         x

and of 12:

111111111122222222223333333333444444444455555555556
123456789012345678901234567890123456789012345678901234567890
           x           x           x           x           x

Then they will match up at 60!

Now if we think that each of these numbers represent 1/(10*12) second, it becomes a bit easy to reason about this.

This will mean that every 10 units of time, the 12Hz engine bursts. (the faster one)
and every 12 units of time, the 10Hz engine bursts (the slower one).

So we have our answer here! Every 60 units of time, they burst together. That means every 60 / (10 * 12) seconds = 1/2 seconds.

So we hear the "beats" every 2 seconds!

This is also the GCD of 10 and 12 which you were looking for actually, not the LCM!

</pre>

Sun, 19 Apr 2020 10:18 GMT