each ˈother S1 W1 pronoun [not used as the subject of a sentence]
used to show that each of two or more people does something to the other or others ⇒ one another:
Susan and Robert kissed each other passionately.
The girls looked at each other.
They enjoy each other’s company.
⇒ be at each other’s throats at throat(5)

[TahlilGaran] Dictionary of Contemporary English ▲

each other
pronoun
1.
BAD: I hope that you will both write to each others.
GOOD: I hope that you will both write to each other.

Usage Note:
Each other has no plural form: 'We've been writing letters to each other for the last two years.'

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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.

Usage Note:
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)

[TahlilGaran] Dictionary of Common Errors ▲

each other
pron. Each one the other; one the other.
That man and his wife love each other.
Bill and Mary gave one another Christmas presents last year.
All the children at the party were looking at one another trying to recognize one another in their masks and costumes.
The birds fought each other over the bread.

[TahlilGaran] English Idioms Dictionary ▲