2023 AMC 12B Problems/Problem 15

Problem

Suppose that $a,b,$ and $c$ are positive integers such that $\frac{a}{14}+\frac{b}{15}=\frac{c}{210}$ Which of the following statements are necessarily true?

$\textbf{(A) }\text{I, II, and III}\qquad\textbf{(B) }\text{I only}\qquad\textbf{(C) }\text{I and II only}\qquad\textbf{(D) }\text{III only}\qquad\textbf{(E) }\text{II and III only}$

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2023 AMC 12B Problems/Problem 15

Problem