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Combinatorics Difficulty 3.0 AMC 10/12 Find the answer United Kingdom

Sixty apples and sixty pears are to be packed into boxes so that each box contains the same number of apples, and no two boxes contain the same number of pears. What is the largest possible number of boxes that can be packed in this way?

(A) $20$ (B) $15$ (C) $12$ (D) $10$ (E) $6$

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