The lengths of the sides of a triangle are given by three integers \( A \), \( B \), and \( C \). The Least Common Multiple (LCM) of \( A \) and \( B \) is 84, and the Greatest Common Divisor (GCD) of \( B \) and \( C \) is 7. If \( A \), \( B \), and \( C \) are distinct and the sum \( A + B + C \) is a two-digit prime number, find \( A + B + C \). Let's think step by step and output the final answer within \boxed{}.
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