Usage of 'into which'?

Solution 1:

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.