At a textile factory in Fergana, two machines need regular maintenance. The loom is stopped for cleaning every 6 days. The dyeing machine is stopped for inspection every 8 days. Both were stopped on the first of the month.
Each stop costs the factory a shift of work, and the production manager, Malika, wanted the two stops to happen on the same day again as soon as possible, so that the workers could be moved to other tasks once instead of twice.
A junior engineer suggested multiplying: six times eight is forty-eight, so the machines would meet again in 48 days. Malika shook her head. "That is a day they meet," she said, "but not the first one."
She wrote the stops for the loom: days 6, 12, 18, 24. Then for the dyeing machine: days 8, 16, 24. The first number on both lists was 24. Six and eight share a factor of two, so the product counts that two twice.
The factory now plans one combined stop every 24 days, and one separate stop for each machine in between. Over a year, the change saves several shifts of production. The junior engineer now checks for a shared factor before he multiplies any two schedules together.