---
id: 5900f52c1000cf542c51003f
title: 'Problem 448: Average least common multiple'
challengeType: 5
forumTopicId: 302120
dashedName: problem-448-average-least-common-multiple
---

# --description--

The function lcm(a,b) denotes the least common multiple of a and b.

Let A(n) be the average of the values of lcm(n,i) for 1≤i≤n.

E.g: A(2)=(2+2)/2=2 and A(10)=(10+10+30+20+10+30+70+40+90+10)/10=32.

Let S(n)=∑A(k) for 1≤k≤n. S(100)=122726.

Find S(99999999019) mod 999999017.

# --hints--

`euler448()` should return 106467648.

```js
assert.strictEqual(euler448(), 106467648);
```

# --seed--

## --seed-contents--

```js
function euler448() {

  return true;
}

euler448();
```

# --solutions--

```js
// solution required
```