Complex numbers and Roots of unity I have no clue how to begin these problems. How do I start? I don't think I should pound em out...Thanks.
Let P be the set of $42^{\text{nd}}$ roots of unity, and let Q be the set of $70^{\text{th}} $ roots of unity. How many elements do P and Q have in common?
Let P be the set of $42^{\text{nd}} $roots of unity, and let Q be the set of $70^{\text{th}} $roots of unity. What is the smallest positive integer n for which all the elements in P and all the elements in Q are $n^{\text{th}}$ roots of unity?

The first question is the same as asking for which positive integers $k<42$ and $n<70$ do we have $\dfrac{2\pi}{42}k=\dfrac{2\pi}{70}n\iff5k=3n$. The second is equivalent to determining the least common multiple of $42$ and $70$, which is $210$.
