The answer depends on whether “others” refers to the singular or plural possessive. If you are using each other (singular), then it is “each other’s.” If you are using the plural, then the apostrophe goes after the “s.”

However, you should point out to students that each other is treated as a singular pronoun and emphasizes two or more separate people. Each other’s is always correct, and each others’ is never correct.

Other’s and others’ are both correct forms of the word “other.” Use others when referring to a group of people or things, such as “The others are waiting for you outside.” Use others’ for plural possessive form, such as “The others’ opinions are very important to me.” Other’s acts as the singular possessive form.