2024 Mock AMC 10 - Problem 5

Given fractions \frac{a}{15} and \frac{b}{21} that are already in lowest terms (i.e. \frac{a}{15} and \frac{b}{21} cannot be reduced further), find the smallest value of the denominator of \frac{a}{15} + \frac{b}{21}, when this fraction is reduced.

\textbf{(A) }3\qquad\textbf{(B) }5\qquad\textbf{(C) }7\qquad\textbf{(D) }35\qquad\textbf{(E) }105