I was asked earlier where the apostrophe went in a sentence like "They checked each other's work". One common misconception is that since the pronoun they is plural, then each other is plural too, so the apostrophe goes after the s like for plural nouns (the employees' work, the students' work).
In fact, each other behaves as a singular pronoun (even though there must, by default, be more than one person involved), so when it comes to inserting an apostrophe, it behaves like most singular nouns (by adding 's).
I've checked in Collins and the Oxford Dictionary of English and although they each have an entry for 'each other', plus an example, it is not an example with an apostrophe, so not terribly helpful. Fowler is quite clear that it cannot be others', and has the example "A lot of old cats ready to tear each other's eyes out".