Does the following sentence sound awkward because of the positioning of whom?
Beans grew up in a Roman Catholic household with four brothers; the least successful of whom was the bank president.
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I have no reference, but I've heard the claim that whom should be used when referring to people, and which the rest of the time.
In any case, the sentence sounds fine to me. I easily understand what the writers intention is.
The OP asks if the sentence sounds awkward because of the positioning of whom. The only alternative word order is of whom the least successful was the bank president. That seems to me to give a different emphasis, suggesting that the other three brothers might have been moderately successful. By beginning the clause with the least successful, he suggests that none of them might have been up to much.
As for whom versus which, the corpus-based ‘Longman Student Grammar of Spoken and Written English’ (based on the big Longman Grammar) says: