76 lines
2.9 KiB
Markdown
76 lines
2.9 KiB
Markdown
---
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id: 5a23c84252665b21eecc7edf
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title: Least common multiple
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challengeType: 5
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---
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## Description
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<section id='description'>
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The least common multiple of 12 and 18 is 36, because 12 is a factor (12 × 3 = 36), and 18 is a factor (18 × 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.
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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>.
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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>.
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\( \operatorname{lcm}(m, n) = \frac{|m \times n|}{\operatorname{gcd}(m, n)} \)
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</section>
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## Instructions
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<section id='instructions'>
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Compute the least common multiple of an array of intergers.
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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.
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</section>
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## Tests
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<section id='tests'>
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``` yml
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tests:
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- text: <code>LCM</code> should be a function.
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testString: assert(typeof LCM == 'function', '<code>LCM</code> should be a function.');
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- text: <code>LCM([2, 4, 8])</code> should return a number.
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testString: assert(typeof LCM([2, 4, 8]) == 'number', '<code>LCM([2, 4, 8])</code> should return a number.');
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- text: <code>LCM([2, 4, 8])</code> should return <code>8</code>.
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testString: assert.equal(LCM([2, 4, 8]), 8, '<code>LCM([2, 4, 8])</code> should return <code>8</code>.');
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- text: <code>LCM([4, 8, 12])</code> should return <code>24</code>.
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testString: assert.equal(LCM([4, 8, 12]), 24, '<code>LCM([4, 8, 12])</code> should return <code>24</code>.');
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- text: <code>LCM([3, 4, 5, 12, 40])</code> should return <code>120</code>.
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testString: assert.equal(LCM([3, 4, 5, 12, 40]), 120, '<code>LCM([3, 4, 5, 12, 40])</code> should return <code>120</code>.');
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- text: <code>LCM([11, 33, 90])</code> should return <code>990</code>.
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testString: assert.equal(LCM([11, 33, 90]), 990, '<code>LCM([11, 33, 90])</code> should return <code>990</code>.');
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- text: <code>LCM([-50, 25, -45, -18, 90, 447])</code> should return <code>67050</code>.
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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>.');
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```
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</section>
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## Challenge Seed
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<section id='challengeSeed'>
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<div id='js-seed'>
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```js
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function LCM(A) {
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// Good luck!
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}
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```
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</div>
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</section>
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## Solution
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<section id='solution'>
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```js
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function LCM (A) {
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var n = A.length, a = Math.abs(A[0]);
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for (var i = 1; i < n; i++)
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{ var b = Math.abs(A[i]), c = a;
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while (a && b){ a > b ? a %= b : b %= a; }
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a = Math.abs(c*A[i])/(a+b);
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}
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return a;
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}
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```
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</section>
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