algorithm: lcm (#68)

Co-authored-by: patrickwestervelt <[email protected]>

Author: Psytew

Maths/LowestCommonMultiple.ts

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+/**
+ * @function LowestCommonMultiple
+ * @description Determine the lowest common multiple of a group of numbers.
+ * @param {Number[]} nums - An array of numbers.
+ * @return {Number} - The lowest common multiple.
+ * @see https://www.mathsisfun.com/least-common-multiple.html
+ * @example LowestCommonMultiple(3, 4) = 12
+ * @example LowestCommonMultiple(8, 6) = 24
+ * @example LowestCommonMultiple(5, 8, 3) = 120
+ */
+
+import { greatestCommonFactor } from "./GreatestCommonFactor";
+
+//A naive solution which requires no additional mathematical algorithm
+
+export const naiveLCM = (nums: number[]): number => {
+  if (nums.some((num) => num < 0)) {
+    throw new Error("numbers must be positive to determine lowest common multiple");
+  }
+
+  if (nums.length === 0) {
+    throw new Error("at least one number must be passed in");
+  }
+
+  const max_num = Math.max(...nums);
+  let current_num = max_num;
+
+  while (true) {
+    if (nums.every((num) => current_num % num === 0)){
+      return current_num;
+    } else {
+      current_num += max_num;
+    }
+  }
+}
+
+//A typically more efficient solution which requires prior knowledge of GCF
+//Note that due to utilizing GCF, which requires natural numbers, this method only accepts natural numbers.
+
+export const binaryLCM = (a: number, b: number): number => {
+  if (a < 0 || b < 0) {
+    throw new Error("numbers must be positive to determine lowest common multiple");
+  }
+
+  if (!Number.isInteger(a) || !Number.isInteger(b)) {
+    throw new Error("this method, which utilizes GCF, requires natural numbers.");
+  }
+
+  return a * b / greatestCommonFactor([a, b]);
+}
+
+export const lowestCommonMultiple = (nums: number[]): number => {
+  if (nums.length === 0) {
+    throw new Error("at least one number must be passed in");
+  }
+
+  return nums.reduce(binaryLCM);
+}

Maths/test/LowestCommonMultiple.test.ts

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+import { binaryLCM, lowestCommonMultiple, naiveLCM } from "../LowestCommonMultiple";
+
+describe("naiveLCM", () => {
+  test.each([[[3, 4], 12], [[8, 6], 24], [[5, 8, 3], 120], [[0.8, 0.4], 0.8]])(
+    "of given two numbers is correct",
+    (nums, expected) => {
+      expect(naiveLCM(nums)).toBe(expected);
+    },
+  );
+
+  test("only positive numbers should be accepted", () => {
+    expect(() => naiveLCM([-2, -3])).toThrowError(
+      "numbers must be positive to determine lowest common multiple",
+    );
+  });
+
+  test("at least one number must be passed in", () => {
+    expect(() => naiveLCM([])).toThrowError(
+      "at least one number must be passed in",
+    );
+  });
+});
+
+describe("binaryLCM", () => {
+  test.each([[3, 4, 12], [8, 6, 24], [8, 16, 16]])(
+    "of given two numbers is correct",
+    (numa, numb, expected) => {
+      expect(binaryLCM(numa, numb)).toBe(expected);
+    },
+  );
+
+  test("only whole numbers should be accepted", () => {
+    expect(() => binaryLCM(-2, -3)).toThrowError(
+      "numbers must be positive to determine lowest common multiple",
+    );
+  });
+});
+
+describe("lowestCommonMultiple", () => {
+  test.each([[[3, 4], 12], [[8, 6], 24], [[5, 8, 3], 120], [[8, 16], 16]])(
+    "of given two numbers is correct",
+    (nums, expected) => {
+      expect(lowestCommonMultiple(nums)).toBe(expected);
+    },
+  );
+
+  test("only positive numbers should be accepted", () => {
+    expect(() => lowestCommonMultiple([-2, -3])).toThrowError(
+      "numbers must be positive to determine lowest common multiple",
+    );
+  });
+
+  test("at least one number must be passed in", () => {
+    expect(() => lowestCommonMultiple([])).toThrowError(
+      "at least one number must be passed in",
+    );
+  });
+});