Let $R$ be the set of primitive $42^{\text{nd}}$ roots of unity, and let $S$ be the set of primitive $70^{\text{th}}$ roots of unity. How many elements do $R$ and $S$ have in common?

\(GCF(42,70)=7\\ \text{Thus the common roots of unity are}\\ \Large e^{\pm i 2\pi \frac{k}{7}},~\normalsize k=0,1,\dots ,6\)

\(\text{There are 14 of these}\)