# Problem 347: Largest integer divisible by two primes

![graphic](img347.gif)

The largest integer ≤ 100 that is only divisible by both the primes 2
and 3 is 96, as 96=32\*3=25\*3. For two distinct primes p and q let
M(p,q,N) be the largest positive integer ≤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 ≤ 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(10 000 000).