2023 AMC 10 B

Suppose a, b, and c are positive integers such that

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. (2023 AMC10B Q18)