Cosets and Lagrange's Theorem · Hard problem

A group $G$ has order $210$. It has subgroups $H$ of order $70$ and $K$ of order $42$. Since $H\cap K$ is a subgroup of both, $|H\cap K|$ divides $\gcd(70,42)=14$. Also, the set $HK=\{hk : h\in H, k\in K\}$ has exactly $|H||K|/|H\cap K|$ elements, which cannot exceed $|G|=210$. What must $|H\cap K|$ be?