Least Common Multiple (LCM)

Least Common Multiple.js

// Least Common Multiple

function LCM(n, m, range) {

    var list1 = [];
    var list2 = [];

    var match;
    for(var i = 1; i <= range; i++) {
        list1.push(n*i)
        list2.push(m*i)

        //compare two arrays, if there is a match this loop will break because this will be the LCM
        var match = findMatch(list1, list2);
        if(match !== 0) break;
    }

    return match;
}
// compare each item in the two arrays in the current state, and return the first match.
function findMatch(arr1, arr2) {
    var num = 0;
    for(var i = 0; i< arr1.length; i++) {
        for( var y = 0; y < arr2.length; y++ ) {
            if (arr1[i] === arr2[y]) {
                num = arr1[i];
                break;
            }
        }
    }

    return num;
}


// To find the LCM with the Euclidean Algorithm like we can do with GCF.
// Just use the equation LCM(a, b) = (a*b)/GCF(a,b)

function LCM2(a, b){
    return (a*b)/GCF2(a,b)
}


// You can find the code bellow from this gist https://gist.github.com/NouranMahmoud/7c9cb828c43287b9a74f0085242fcba9
function GCF2(num1, num2) {
    var gcf =  recursion(num1, num2);
    return gcf;
}

function recursion(num1, num2) {
    // the equation is num1 =  Math.floor(num1/num2)*num2 + remainder;
    // but I chanegd it to be able to store the remainder .. which will be our GCF.
    var remainder = num1 - Math.floor(num1/num2)*num2;
    
    // if remainder if 0, then we need the previous remainder which is num2
    if(remainder === 0) {
        return num2;
    }
    

    num1 = num2;
    num2 = remainder;

    return recursion(num1, num2); // re calculate with the new values.
}