Add lcm.

Author: trekhleb

README.md

@@ -33,10 +33,9 @@
   * [Power Set](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/math/power-set)
   * [Primality Test](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/math/primality-test) (trial division)
   * [Euclidean Algorithm](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/math/euclidean-algorithm) - calculate the greatest common divisor (GCD)
+  * [Least Common Multiple (LCM)](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/math/least-common-multiple)
   * [Fisher–Yates Shuffle](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/math/fisher-yates) - random permutation of a finite sequence
   * Collatz Conjecture algorithm
-  * Greatest Difference
-  * Least Common Multiple
   * Newton's square
   * Shannon Entropy
 * **String**

src/algorithms/math/euclidean-algorithm/__test__/euclieanAlgorithm.test.js

@@ -20,5 +20,7 @@ describe('euclideanAlgorithm', () => {
     expect(euclideanAlgorithm(105, 252)).toBe(21);
     expect(euclideanAlgorithm(1071, 462)).toBe(21);
     expect(euclideanAlgorithm(462, 1071)).toBe(21);
+    expect(euclideanAlgorithm(462, -1071)).toBe(21);
+    expect(euclideanAlgorithm(-462, -1071)).toBe(21);
   });
 });

src/algorithms/math/euclidean-algorithm/euclideanAlgorithm.js

@@ -1,9 +1,12 @@
 /**
- * @param {number} a
- * @param {number} b
+ * @param {number} originalA
+ * @param {number} originalB
  * @return {number|null}
  */
-export default function euclideanAlgorithm(a, b) {
+export default function euclideanAlgorithm(originalA, originalB) {
+  const a = Math.abs(originalA);
+  const b = Math.abs(originalB);
+
   if (a === 0 && b === 0) {
     return null;
   }
@@ -16,9 +19,14 @@ export default function euclideanAlgorithm(a, b) {
     return a;
   }
 
+  // Normally we need to do subtraction (a - b) but to prevent
+  // recursion occurs to often we may shorten subtraction to (a % b).
+  // Since (a % b) is normally means that we've subtracted b from a
+  // many times until the difference became less then a.
+
   if (a > b) {
-    return euclideanAlgorithm(a - b, b);
+    return euclideanAlgorithm(a % b, b);
   }
 
-  return euclideanAlgorithm(b - a, a);
+  return euclideanAlgorithm(b % a, a);
 }

src/algorithms/math/least-common-multiple/README.md

@@ -0,0 +1,62 @@
+# Least common multiple
+
+In arithmetic and number theory, the least common multiple, 
+lowest common multiple, or smallest common multiple of 
+two integers `a` and `b`, usually denoted by `LCM(a, b)`, is 
+the smallest positive integer that is divisible by 
+both `a` and `b`. Since division of integers by zero is 
+undefined, this definition has meaning only if `a` and `b` are 
+both different from zero. However, some authors define `lcm(a,0)`
+as `0` for all `a`, which is the result of taking the `lcm`
+to be the least upper bound in the lattice of divisibility.
+
+## Example
+
+What is the LCM of 4 and 6?
+
+Multiples of `4` are:
+
+```
+4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, ...
+```
+
+and the multiples of `6` are:
+
+```
+6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, ...
+```
+
+Common multiples of `4` and `6` are simply the numbers 
+that are in both lists:
+
+```
+12, 24, 36, 48, 60, 72, ....
+```
+
+So, from this list of the first few common multiples of 
+the numbers `4` and `6`, their least common multiple is `12`.
+
+## Computing the least common multiple
+
+The following formula reduces the problem of computing the 
+least common multiple to the problem of computing the greatest 
+common divisor (GCD), also known as the greatest common factor:
+
+```
+lcm(a, b) = |a * b| / gcd(a, b)
+```
+
+![LCM](https://upload.wikimedia.org/wikipedia/commons/c/c9/Symmetrical_5-set_Venn_diagram_LCM_2_3_4_5_7.svg)
+
+A Venn diagram showing the least common multiples of 
+combinations of `2`, `3`, `4`, `5` and `7` (`6` is skipped as 
+it is `2 × 3`, both of which are already represented).
+
+For example, a card game which requires its cards to be 
+divided equally among up to `5` players requires at least `60`
+cards, the number at the intersection of the `2`, `3`, `4`
+and `5` sets, but not the `7` set.
+
+## References
+
+[Wikipedia](https://en.wikipedia.org/wiki/Least_common_multiple)

src/algorithms/math/least-common-multiple/__test__/leastCommonMultiple.test.js

@@ -0,0 +1,18 @@
+import leastCommonMultiple from '../leastCommonMultiple';
+
+describe('leastCommonMultiple', () => {
+  it('should find least common multiple', () => {
+    expect(leastCommonMultiple(0, 0)).toBe(0);
+    expect(leastCommonMultiple(1, 0)).toBe(0);
+    expect(leastCommonMultiple(0, 1)).toBe(0);
+    expect(leastCommonMultiple(4, 6)).toBe(12);
+    expect(leastCommonMultiple(6, 21)).toBe(42);
+    expect(leastCommonMultiple(7, 2)).toBe(14);
+    expect(leastCommonMultiple(3, 5)).toBe(15);
+    expect(leastCommonMultiple(7, 3)).toBe(21);
+    expect(leastCommonMultiple(1000000, 2)).toBe(1000000);
+    expect(leastCommonMultiple(-9, -18)).toBe(18);
+    expect(leastCommonMultiple(-7, -9)).toBe(63);
+    expect(leastCommonMultiple(-7, 9)).toBe(63);
+  });
+});

src/algorithms/math/least-common-multiple/leastCommonMultiple.js

@@ -0,0 +1,15 @@
+import euclideanAlgorithm from '../euclidean-algorithm/euclideanAlgorithm';
+
+/**
+ * @param {number} a
+ * @param {number} b
+ * @return {number}
+ */
+
+export default function leastCommonMultiple(a, b) {
+  if (a === 0 && b === 0) {
+    return 0;
+  }
+
+  return Math.abs(a * b) / euclideanAlgorithm(a, b);
+}