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curriculum/challenges/english/10-coding-interview-prep/rosetta-code/least-common-multiple.md

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+---
+id: 5a23c84252665b21eecc7edf
+title: Least common multiple
+challengeType: 5
+forumTopicId: 302301
+---
+
+## 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="https://rosettacode.org/wiki/greatest common divisor" target="_blank">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 integers.
+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');
+  - text: <code>LCM([2, 4, 8])</code> should return a number.
+    testString: assert(typeof LCM([2, 4, 8]) == 'number');
+  - text: <code>LCM([2, 4, 8])</code> should return <code>8</code>.
+    testString: assert.equal(LCM([2, 4, 8]), 8);
+  - text: <code>LCM([4, 8, 12])</code> should return <code>24</code>.
+    testString: assert.equal(LCM([4, 8, 12]), 24);
+  - text: <code>LCM([3, 4, 5, 12, 40])</code> should return <code>120</code>.
+    testString: assert.equal(LCM([3, 4, 5, 12, 40]), 120);
+  - text: <code>LCM([11, 33, 90])</code> should return <code>990</code>.
+    testString: assert.equal(LCM([11, 33, 90]), 990);
+  - 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);
+```
+
+</section>
+
+## Challenge Seed
+
+<section id='challengeSeed'>
+
+<div id='js-seed'>
+
+```js
+function LCM(A) {
+
+}
+```
+
+</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>