Arthur Christmas and the Least Common Multiple

I left Arthur Christmas and Grand-Santa in a hypothetical puzzle, inspired by the movie, with them stranded on a tiny island while their team of flying reindeer and sleigh carried on in a straight line without them. I am assuming for the sake of an interesting problem that this means the reindeer are carrying on the Great Circle route, favored by airplanes and satellites, and that the reindeer are in an orbit more like the satellite’s than the reindeers — that is, they keep to a circle in a plane which isn’t rotating while the Earth does, since otherwise, Arthur and Grand-Santa have to wait only for the reindeer to finish one lap around the planet and somehow get up to flying altitude to be picked up. If the reindeer aren’t rotating the with the Earth, then, when the reindeer finish one circuit our heroes are going to be … well, maybe east, maybe west, of the reindeer; the problem is, they’re going to be away.

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