Part of the reason for that is that LIGO isn't exactly a Michaelson interferometer in that it has an extra pair of mirrors in each arm. If you look at this schematic [1] then in a traditional Michaelson interferometer you would only have the mirrors that are at the end of both arms.
With LIGO there is an extra set of mirrors within the arms this allows the light from the laser to bounce between them ~100 times or so increasing the effective path length greatly.
[1] https://www.nsf.gov/news/speeches/colwell/rc03_ligo/img009.j...
