Both 'to each other' and 'with each other' are correct, but they are used in different contexts. 'To each other' is used to indicate a reciprocal action or relationship between two or more entities, while 'with each other' is used to show a joint action or interaction between the entities.

The correct way to spell the phrase is ‘each other’. It should always be two separate words, not combined into one. This phrase is used when talking about two or more people or things affecting or relating to one another. A common mistake is writing it as ‘eachother’, but this is incorrect in English.

Some English usage authorities urge the use of each other when referring to two people and one another for more than two people. Yet there’s no logical reason for this guideline, and writers break it nearly as often as they follow it. In practice, the two phrases are interchangeable.