Create 005.js

Author: Walker30263

Diff for: 005.js

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+/*
+Source: https://projecteuler.net/problem=5
+
+Problem:
+"2520 is the smallest number that can be divided by each of the numbers from 1 to 10 without any remainder.
+
+What is the smallest positive number that is evenly divisible by all of the numbers from 1 to 20?"
+
+
+My Algorithm:
+
+This is actually doable without code using number theory, but since this is a GitHub repository with JS solutions, here's the JS algorithm:
+
+1. Define a function to check if number is evenly divisble by all numbers from 1 to 20
+2. Use a while loop to increment i by the product of all prime numbers from 1 to 20, since the number has to be a multiple of all the prime numbers from 1 to 20 if it is evenly divisible by all numbers from 1 to 20
+3. End the loop when it's divisble by all numbers from 1 to 20
+*/
+
+function isEvenlyDivisble(x) {
+  for (let i = 1; i <= 20; i++) {
+    if (x % i !== 0) { //if the remainder is not 0, it's not evenly divisble, so return false
+      return false;
+    }
+  }
+
+  return true; //if the number survived through all 20 divisbility trials in the for-loop, then return true
+}
+
+function solution() {
+  let incrementBy = 2*3*5*7*11*13*17*19; //product of all prime numbers from 1-20
+  
+  let i = 0;
+  while ((!isEvenlyDivisble(i)) || (i === 0)) { //while i isn't evenly divisible or if i is 0 (it's initial value)...
+    i += incrementBy; //add it by the product of all prime numbers from 1-20
+  }
+  
+  return i; //when i is evenly divisble, return it, we now have the answer!
+}
+
+console.log(solution()); //the answer!