pronoun
1
BAD : I hope that you will both write to each others.
GOOD : I hope that you will both write to each other.
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Each other has no plural form: 'We've been writing letters to each other for the last two years.'
2
BAD : We had to describe the pictures each other.
GOOD : We had to describe the pictures to each other.
BAD : They live a long way each other.
GOOD : They live a long way from each other.
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You use prepositions in front of each other (pronoun) in the same way as you use prepositions in front of him, her, us etc. Compare: 'We talked to her.' 'We talked to each other.'
See also ONE ANOTHER (↑ one another )