---
id: 5a23c84252665b21eecc7edf
title: Least common multiple
challengeType: 5
---

## Description
<section id='description'>
The least common multiple of 12 and 18 is 36, because 12 is a factor (12 &times; 3 = 36), and 18 is a factor (18 &times; 2 = 36), and there is no positive integer less than 36 that has both factors.  As a special case, if either  <i>m</i>  or  <i>n</i>  is zero, then the least common multiple is zero.
One way to calculate the least common multiple is to iterate all the multiples of  <i>m</i>,  until you find one that is also a multiple of  <i>n</i>.
If you already have  <i>gcd</i>  for <a href="http://rosettacode.org/wiki/greatest common divisor">greatest common divisor</a>,  then this formula calculates  <i>lcm</i>.
\( \operatorname{lcm}(m, n) = \frac{|m \times n|}{\operatorname{gcd}(m, n)} \)
</section>

## Instructions
<section id='instructions'>
Compute the least common multiple of an array of intergers.
Given  <i>m</i>  and  <i>n</i>,  the least common multiple is the smallest positive integer that has both  <i>m</i>  and  <i>n</i>  as factors.
</section>

## Tests
<section id='tests'>

``` yml
tests:
  - text: <code>LCM</code> should be a function.
    testString: assert(typeof LCM == 'function', '<code>LCM</code> should be a function.');
  - text: <code>LCM([2, 4, 8])</code> should return a number.
    testString: assert(typeof LCM([2, 4, 8]) == 'number', '<code>LCM([2, 4, 8])</code> should return a number.');
  - text: <code>LCM([2, 4, 8])</code> should return <code>8</code>.
    testString: assert.equal(LCM([2, 4, 8]), 8, '<code>LCM([2, 4, 8])</code> should return <code>8</code>.');
  - text: <code>LCM([4, 8, 12])</code> should return <code>24</code>.
    testString: assert.equal(LCM([4, 8, 12]), 24, '<code>LCM([4, 8, 12])</code> should return <code>24</code>.');
  - text: <code>LCM([3, 4, 5, 12, 40])</code> should return <code>120</code>.
    testString: assert.equal(LCM([3, 4, 5, 12, 40]), 120, '<code>LCM([3, 4, 5, 12, 40])</code> should return <code>120</code>.');
  - text: <code>LCM([11, 33, 90])</code> should return <code>990</code>.
    testString: assert.equal(LCM([11, 33, 90]), 990, '<code>LCM([11, 33, 90])</code> should return <code>990</code>.');
  - text: <code>LCM([-50, 25, -45, -18, 90, 447])</code> should return <code>67050</code>.
    testString: assert.equal(LCM([-50, 25, -45, -18, 90, 447]), 67050, '<code>LCM([-50, 25, -45, -18, 90, 447])</code> should return <code>67050</code>.');
```

</section>

## Challenge Seed
<section id='challengeSeed'>
<div id='js-seed'>

```js
function LCM(A) {
  // Good luck!
}
```

</div>
</section>

## Solution
<section id='solution'>

```js
function LCM (A) {
    var n = A.length, a = Math.abs(A[0]);
    for (var i = 1; i < n; i++)
     { var b = Math.abs(A[i]), c = a;
       while (a && b){ a > b ? a %= b : b %= a; }
       a = Math.abs(c*A[i])/(a+b);
     }
    return a;
}
```

</section>