---
id: 5900f4c81000cf542c50ffd9
title: 'Problem 347: Largest integer divisible by two primes'
challengeType: 5
forumTopicId: 302006
dashedName: 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\*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).

# --hints--

`euler347()` should return 11109800204052.

```js
assert.strictEqual(euler347(), 11109800204052);
```

# --seed--

## --seed-contents--

```js
function euler347() {

  return true;
}

euler347();
```

# --solutions--

```js
// solution required
```