Open up an Associated Press Stylebook to the letter E and the very first entry you see is "each. Takes a singular verb." (At least, it's the first entry in the 1992 version I happen to have handy.)
So when we copy editors think of the word "each," we think of matters such as: There are 50 units, and each has (not have) stunning views.
The problem is that this only applies to "each" the pronoun. But each has other forms:
The college of engineering, college of business, and college of arts and letters each require department approval for admission.
If you're thinking like a copy editor (or at least a copy editor on autopilot), you'll hesitate at that each, as I did recently. Each is singular -- it says so right here in my AP Stylebook. Therefore, that should be "each requires," right?
This each is not a pronoun. It's an adverb. (It can also be an adjective.) So the subject of our example sentence is "the college of engineering, college of business, and college of arts and letters." It's a plural subject, in no way altered by that adverbial "each." Thus, the correct verb conjugation is "require."
Just somethin' on my mind as I head to lunch ....