/**

* @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 => {

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)

}