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2023 AMC 12B Problems/Problem 15

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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?

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

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