Let's start with a really simple rhythm, where you have a drum hit followed by silence, for a total of 8 beats. Try it!
Our 8 beat cycle is a little boring, sure. But now let's add a 2 beat cycle. We will do two maracas shakes in a row. Because it is only two beats long, we have to repeat it 4 times so that it matches up with the big cycle of 8.
Now you have the basic concept. A two-beat cycle would fit an 8 beat cycle if you repeat it 4 times, because 2X4 = 8. A 3 beat cycle would fit a 9 beat cycle if you repeat it 3 times, because 3X3 = 9.
What if you had a 3 beat cycle and a 4 beat cycle? Try the example below and see if you can get the two wheels to stop at the same time by adjusting the number of repeats.
Fitting musical cycles into the LCM is the key to rhythms in salsa, reggae, hiphop, and more. Nearly every form of modern pop music uses LCM. Because the Carribean was first stop in the Atlantic slave trade, that is where many of these forms that mixed African polyrythms with European instruments were born.