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.”

“Each others” is used when you’re referring to the plural form of “each other.” However, there is no plural form of “each other,” so “each others” is actually an incorrect term that can’t be used.

They helped one another up. / They helped each other up. The couple enjoyed each other’s company. / The couple enjoyed one another’s company.