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id	title	challengeType	forumTopicId	dashedName
5900f4c81000cf542c50ffd9	Problem 347: Largest integer divisible by two primes	5	302006	problem-347-largest-integer-divisible-by-two-primes

--description--

The largest integer ≤ 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 ≤ 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).

--hints--

integerDivisibleByTwoPrimes() should return 11109800204052.

assert.strictEqual(integerDivisibleByTwoPrimes(), 11109800204052);

--seed--

--seed-contents--

function integerDivisibleByTwoPrimes() {

  return true;
}

integerDivisibleByTwoPrimes();

--solutions--

// solution required

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