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

## Description
<section id='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.
</section>

## Instructions
<section id='instructions'>

</section>

## Tests
<section id='tests'>

```yml
tests:
  - text: <code>euler448()</code> should return 106467648.
    testString: assert.strictEqual(euler448(), 106467648);

```

</section>

## Challenge Seed
<section id='challengeSeed'>

<div id='js-seed'>

```js
function euler448() {
  // Good luck!
  return true;
}

euler448();

```

</div>

</section>

## Solution
<section id='solution'>

```js
// solution required
```

</section>