each other

noun

each the other; one another (used as a compound reciprocal pronoun):

to strike at each other; to hold each other's hands; to love each other.

Origin

before 1000; Middle English; Old English. See each, other

Usage note

Although some insist that each other be used only in reference to two (The two candidates respected each other) and one another in reference to three or more (The three nations threaten one another), in standard practice they are interchangeable. Each other is not restricted to two, nor is one another restricted to three or more.
The possessive of each other is each other's; the possessive of one another is one another's.

Examples from the web for each other

Mount two inexpensive mirrored cabinets next to each other to create one seamless surface.
Choose any large pot and umbrella that match your garden decor and coordinate with each other.
Hold the posts plumb by placing diagonal braces at right angles to each other.
Left undisturbed, they'd glom onto each other and become a fortress of twisted shells.
Our goals were to open the spaces to each other and to turn the kitchen into a warm and elegant entertaining area.
These branches should be well spaced along the trunk and should radiate in different directions so they don't shade each other.
Use a tighter-than-usual spacing method for seedlings so that plants will support each other and protect foliage from sunburn.
Or, if the other queen has emerged by the time they find each other, they will often fight until one is dead.
Players should line up in two lines, with partners facing each other.
The books discuss topics such as how people greet each other, customs used at the dinner table, and business etiquette.

British Dictionary definitions for each other

each other

pronoun

used when the action, attribution, etc, is reciprocal: furious with each other

Usage note

Each other and one another are interchangeable in modern British usage

Word Origin and History for each other

reciprocal pronoun, originally in late Old English a phrase, with each as the subject and other inflected (as it were "each to other," "each from other," etc.).

Idioms and Phrases with each other

each other

Also, one another. Each one the other, one the other, as in The boys like each other, or The birds were fighting one another over the crumbs. Both of these phrases indicate a reciprocal relationship or action between the subjects preceding (the boys, the birds). Formerly, many authorities held that each other should be confined to a relationship between two subjects only and one another used when there are more than two. Today most do not subscribe to this distinction, which was never strictly observed anyway. [ Late 1300s ]

Also see: at each other's throats