Question

What is the shortest distance between two galaxies?

Answer 1

closest to the Milky Way is the Canis Major Dwarf irregular galaxy (disputed) at a distance of ~25,000 light years from the solar system, followed by Sagittarius Dwarf Elliptical Galaxy (not disputed) at about 70,000 light years. There is no limit to how close galaxies can get.

Answer 2

It can be calculated as the distance between the outer most arms of both galaxies