I saw this in an article online today. Where does the apostrophe go?
If you remember that everything in front of the apostrophe has to be a word, you know that it cannot be each others' because there is no such word as each others. There is just one person involved. It is always singular possessive.
...part of each other's lives...
...no need to know each other's business...
Happy punctuating!
Margie