The saros repeats an eclipse every 18 years, but a third of a day out, so the Earth has turned and the shadow lands a third of the way round the world. Wait three saroses and it comes home.

18 years 11 days and 8 hours is the saros; those extra 8 hours are why the same eclipse walks 120 degrees west each time. Three of them together — 54 years and about 34 days, the exeligmos — put the whole number of days back and return the track to roughly the same longitudes. The Antikythera mechanism has a dial for it.