Usage of 'into which'?

Both phrases (they are not sentences) would be precisely equivalent in meaning, if you hadn't changed from a passive to a middle verb.

The first is more literary;

The smallest x which y can be divided into

is much more common in ordinary speech.

There used to be a lot of people who believed that the second was "wrong", and you may still encounter old-fashioned teachers or editors who have this idea.

The change from "can be divided into" to "can divide into" is a completely separate issue , but in this case has little effect on the meaning, and could be applied in either sentence.

They are both fragments of a question that should start with "What is" and end with a question mark. An example would be "What is the smallest x into which y can be divided?" or "What is the smallest x which y can divide into? Even then, since it seems to be some sort of Math problem, in order to answer this question you would still need to know the values of x and y. So you can now think of this sentence fragment as an incomplete Mathematics word problem also.