freeCodeCamp/guide/english/certifications/coding-interview-prep/project-euler/problem-5-smallest-multiple/index.md

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Smallest multiple

Problem 5: Smallest multiple

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Problem Explanation

• In this challenge we need to find the LCM of 1 to n numbers.
• To find LCM of a number we use the following formula:
  • 
• To find GCD (Greatest Common Divisor) of two number we use Euclidean algorithm.
• Once we get LCM of two numbers, we can get LCM of the numbers from 1 to n.

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Solutions

Solution 1 (Click to Show/Hide)

//LCM of two numbers
function lcm(a, b) {
  return (a * b) / gcd(a, b);
}

//Euclidean recursive algorithm
function gcd(a, b) {
  if (b === 0) return a;
  return gcd(b, a % b);
}

function smallestMult(n) {
  let maxLCM = 1;

  //Getting the LCM in the range
  for (let i = 2; i <= n; i++) {
    maxLCM = lcm(maxLCM, i);
  }
  return maxLCM;
}

Relevant Links

• Euclidean algorithm
• LCM