/**
 * @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 "./greatest_common_factor";

//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);
}