The correct spelling is each other’s, not each others. The apostrophe and “s” help show possession by indicating that something belongs to both parties involved. For example, in the sentence “They held each other’s hands,” it means each person held the hands of the other.

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.