The largest integer $\le 100$ that is only divisible by both the primes $2$ and $3$ is $96$, as $96=32\times 3=2^5\times 3$. For two distinct primes $p$ and $q$ let $M(p,q,N)$ be the largest positive integer $\le N$ only divisible by both $p$ and $q$ and $M(p,q,N)=0$ if such a positive integer does not exist.

E.g. $M(2,3,100)=96$.
$M(3,5,100)=75$ and not $90$ because $90$ is divisible by $2$, $3$ and $5$.
Also $M(2,73,100)=0$ because there does not exist a positive integer $\le 100$ that is divisible by both $2$ and $73$.

Let $S(N)$ be the sum of all distinct $M(p,q,N)$. $S(100)=2262$.

Find $S(10000000)$.