Ever notice when you’re behind two cars that have their turn signals on and while they’re currently blinking at alternating intervals, they always seem to sync up and blink at the same time before going back to alternating blinks. How?
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Any two series that don’t have the same period or multiple of the same period will eventually synchronize.
For example suppose we chart their blinks on a number line, one with a period of 7 and other with a period of 3. The slower one blinks at 0, 7, 14, **21**, 28, 35, etc. The faster one blinks on 0, 3, 6, 9, 12, 15, 18, **21**, etc.
Notice how they both blinked on 21, but also consider the lead up to that point. On the faster one’s third blink it is at 6, only 1 unit behind the slower one at 7, but because its period isn’t an even multiple of 7 there will be some remainder that will gradually shift the blink into synchronization.
We can easily figure out where this point is by multiplying the period of one series by the other, in this case 3 x 7 = 21.
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