How to use LCM (Lowest Common Multiple) In Javascript
In this approach, first implement gcd to find the greatest common divisor using Euclid’s algorithm. Implement lcm to calculate the least common multiple as a * b / gcd(a, b). Initialize the answer to 1 and iterate from 2 to n, updating the answer with the least common multiple of the answer and i. After the loop, the answer holds the smallest number divisible by the first n numbers. Return answer.
Example: Demonstration of Finding the the Smallest number that is divisible by first n numbers using LCM (Lowest Common Multiple).
function smallestDivisibleLCM(n) {
function calculateGCD(a, b) {
return b === 0 ? a : calculateGCD(b, a % b);
}
function calculateLCM(a, b) {
return (a * b) / calculateGCD(a, b);
}
// Initialize the result to 1
let answer = 1;
// Iterate through numbers from 2 to n to calculate LCM
for (let i = 2; i <= n; i++) {
answer = calculateLCM(answer, i);
}
return answer;
}
console.log(smallestDivisibleLCM(10));
Output
2520
Time Complexity: O(n * log(n)).
Space Complexity: O(1).
JavaScript Program to Find Smallest Number that is Divisible by First n Numbers
Given a number, our task is to find the smallest number that is evenly divisible by the first n numbers without giving any remainder in JavaScript.
Example:
Input: 10
Output: 2520
Explanation:
2520 is smallest number which is completely divisible by numbers from 1 to 10.
Below are the following approaches for finding the Smallest number that is divisible by the first n numbers:
Table of Content
- Brute Force Approach
- Using LCM (Lowest Common Multiple)