Two clocks tick at different intervals: one every a seconds, one every b seconds. When do they tick together? At every lcm(a, b) seconds.
Example: clock A ticks every 4 seconds, clock B every 6 seconds. They sync at 12, 24, 36... seconds. First sync is lcm(4, 6) = 12.
Any repeating cycle problem uses LCM to find when events align.