Still struggling with smallest common multiple

JavaScript
1

Tell us what’s happening:
I am trying to find the smallest common multiple using the formula:

smallestCommonMultiple = greatestCommonMultiple / largestCommonDivisor

I’ve found greatestCommonMultipler and want to use Euclid’s algorithm for finding the largest common divisor, but when I peek, the solution codes are so short and seem to be using only one formula, where I use two. (I peeked, didn’t read)

I can’t find another formula. Is it because I’m using recursion to find gcm, then using recursion to find gcd, and dividing at the end, when I should really be using recursion to find gcm/gcd each time? (hard to put in words…)

Your code so far


function smallestCommons(arr) {
let x = arr[0];
let y = arr[1];
let array = createArrayFrom(x,y);
console.log(array);

let gcm = greatestCommonMultiple(array);
console.log(gcm);
let gcd = greatestCommonDivisor(array);
console.log(gcd);
let scm = gcm / gcd;

console.log("scm " + scm);
return scm;
}

function createArrayFrom(x,y) {
let array = [];
if (y-x>0) {
  for (let i=y; i>x-1; i--) {array.push(i)}
}
if (x-y>0) {
  for (let i=x; i>y-1; i--) { array.push(i)}
}
return array;
}

function greatestCommonMultiple(array) {
let product = firstProduct(array);
let index = 2;
return checkNumbersRecursively(product, array, index); 
}

function firstProduct(array) {
return array[0] * array[1];
}

function checkNumbersRecursively (product, array, index) {
console.log(index, product)
if (index == array.length) {
  return product;
}
if (product % array[index] != 0) {
  product *= array[index];
}
return checkNumbersRecursively(product, array, index+1);
}

function greatestCommonDivisor(array) {


}

smallestCommons([2,10]);

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Challenge: Smallest Common Multiple

Link to the challenge:

2

I think you are close. These are the usual wikipedia articles that I recommend people look at to get this to the finish line.

  1. lcm(a, b) = a * b / gcd(a, b) (link)
  2. Euclid’s algorithm for GCD (link)
  3. lcm(a, b, c, …) = lcm(a, lcm(b, c, …)) (link)

With the three above pieces, you only need to use recursion when you find the GCD.