Suppose $a$ , $b$ , and $c$ are positive integers such that $$\dfrac{a}{14}+\dfrac{b}{15}=\dfrac{c}{210}.$$

Which of the following statements are necessarily true?

I. If $\gcd(a,14)=1$ or $\gcd(b,15)=1$ or both, then $\gcd(c,210)=1$ .

II. If $\gcd(c,210)=1$ , then $\gcd(a,14)=1$ or $\gcd(b,15)=1$ or both.

III. $\gcd(c,210)=1$ if and only if $\gcd(a,14)=\gcd(b,15)=1$ .