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


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.
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Based on the Random House Dictionary, © Random House, Inc. 2014.
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Collins
World English Dictionary
each other
 
pron
used when the action, attribution, etc, is reciprocal: furious with each other
 
usage  Each other and one another are interchangeable in modern British usage

Collins English Dictionary - Complete & Unabridged 10th Edition
2009 © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins
Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009
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Etymonline
Word Origin & History

each other
reciprocal pronoun, originally in late O.E. a phrase, with each as the subject and other inflected (as it were "each to other," "each from other," etc.).
Online Etymology Dictionary, © 2010 Douglas Harper
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American Heritage
Idioms & Phrases

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.

The American Heritage® Dictionary of Idioms by Christine Ammer.
Copyright © 1997. Published by Houghton Mifflin.
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Example sentences
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.
Idioms & Phrases
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