There is no need for "each other". Whether you're talking to your best friend or talking to a third party about yourself and your best friend, you would just say "We are best friends".
In contexts where you do need to use each other's, that's where the apostrophe always goes—even when there are more than two people. It means 'of each other'.
Ellie Mentary and her brother Rudy check each other's hair for nits every week.
Ali Katt, Dot Matrix and Laurie Park always enjoy each other's company.
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