Program to find LCM of two numbers Last Updated : 23 Jun, 2025 Comments Improve Suggest changes Like Article Like Report Try it on GfG Practice Given two positive integers a and b. Find the Least Common Multiple (LCM) of a and b.LCM of two numbers is the smallest number which can be divided by both numbers. Input : a = 10, b = 5Output : 10Explanation : 10 is the smallest number divisible by both 10 and 5Input : a = 5, b = 11Output : 55Explanation : 55 is the smallest number divisible by both 5 and 11Table of Content[Naive Approach] Using Conditional Loop [Expected Approach] Using GCD LCM Formula[Naive Approach] Using Conditional Loop This approach to calculating the Least Common Multiple (LCM) involves starting from the greater of the two numbers and checking if it's divisible by the smaller number. It iterates through multiples of the larger number, incrementing by the larger number itself in each step. The first multiple that is divisible by the smaller number is the LCM. This method is simple and intuitive, but it can be inefficient, especially for large numbers, as it checks multiple values until a match is found. C++ #include <iostream> #include <algorithm> using namespace std; int lcm(int a, int b) { // larger value int g = max(a, b); // Smaller value int s = min(a, b); for (int i = g; i <= a * b; i += g) { if (i % s == 0) return i; } } int main() { int a = 10, b = 5; cout << lcm(a, b); return 0; } Java class GfG { static int lcm(int a, int b) { // Larger value int g = Math.max(a, b); // Smaller value int s = Math.min(a, b); for (int i = g; i <= a * b; i += g) { if (i % s == 0) return i; } return a * b; } public static void main(String[] args) { int a = 10, b = 5; System.out.println(lcm(a, b)); } } Python def lcm(a, b): # Larger value g = max(a, b) # Smaller value s = min(a, b) for i in range(g, a * b + 1, g): if i % s == 0: return i return a * b if __name__ == '__main__': a = 10 b = 5 print(lcm(a, b)) C# using System; class GfG { static int LCM(int a, int b) { // Larger value int g = Math.Max(a, b); // Smaller value int s = Math.Min(a, b); for (int i = g; i <= a * b; i += g) { if (i % s == 0) return i; } return a * b; } static void Main() { int a = 10, b = 5; Console.WriteLine(LCM(a, b)); } } JavaScript function lcm(a, b) { // Larger value let g = Math.max(a, b); // Smaller value let s = Math.min(a, b); for (let i = g; i <= a * b; i += g) { if (i % s === 0) return i; } return a * b; } // Driver code let a = 10, b = 5; console.log(lcm(a, b)); Output10Time Complexity: O(min(a,b))Auxiliary Space: O(1)[Expected Approach] Using GCD LCM FormulaAn efficient solution is based on the below formula for LCM of two numbers 'a' and 'b'. a x b = LCM(a, b) * GCD (a, b) LCM(a, b) = (a x b) / GCD(a, b)We have discussed function to find GCD of two numbers. Using GCD, we can find LCM. C++ #include <iostream> using namespace std; // function for gcd int gcd(int a, int b) { return (b == 0) ? a : gcd(b, a % b); } int lcm(int a, int b) { return (a / gcd(a, b)) * b; } int main() { int a = 10, b = 5; cout << lcm(a, b); return 0; } Java class GfG { // function for gcd static int gcd(int a, int b) { return (b == 0) ? a : gcd(b, a % b); } static int lcm(int a, int b) { return (a / gcd(a, b)) * b; } public static void main(String[] args) { int a = 10, b = 5; System.out.println(lcm(a, b)); } } Python # function for gcd def gcd(a, b): return a if b == 0 else gcd(b, a % b) def lcm(a, b): return (a // gcd(a, b)) * b if __name__ == '__main__': a = 10 b = 5 print(lcm(a, b)) C# using System; class GfG { static int gcd(int a, int b) { return b == 0 ? a : gcd(b, a % b); } static int lcm(int a, int b) { return (a / gcd(a, b)) * b; } static void Main() { int a = 10, b = 5; Console.WriteLine(lcm(a, b)); } } JavaScript // function for gcd function gcd(a, b) { return b === 0 ? a : gcd(b, a % b); } function lcm(a, b) { return (a / gcd(a, b)) * b; } // Driver code let a = 10, b = 5; console.log(lcm(a, b)); Output10Time Complexity: O(log(min(a,b))Auxiliary Space: O(log(min(a,b)) Java Program to Find LCM of Two Numbers Comment More infoAdvertise with us Next Article LCM of given array elements K kartik Follow Improve Article Tags : Mathematical DSA Basic Coding Problems SAP Labs GCD-LCM +1 More Practice Tags : SAP LabsMathematical Similar Reads GCD (Greatest Common Divisor) Practice Problems for Competitive Programming GCD (Greatest Common Divisor) or HCF (Highest Common Factor) of two numbers is the largest positive integer that divides both of the numbers.GCD of Two NumbersFastest Way to Compute GCDThe fastest way to find the Greatest Common Divisor (GCD) of two numbers is by using the Euclidean algorithm. The E 4 min read Program to Find GCD or HCF of Two Numbers Given two positive integers a and b, the task is to find the GCD of the two numbers.Note: The GCD (Greatest Common Divisor) or HCF (Highest Common Factor) of two numbers is the largest number that divides both of them. Examples:Input: a = 20, b = 28Output: 4Explanation: The factors of 20 are 1, 2, 4 12 min read Check if two numbers are co-prime or not Two numbers A and B are said to be Co-Prime or mutually prime if the Greatest Common Divisor of them is 1. You have been given two numbers A and B, find if they are Co-prime or not.Examples : Input : 2 3Output : Co-PrimeInput : 4 8Output : Not Co-PrimeThe idea is simple, we find GCD of two numbers a 5 min read GCD of more than two (or array) numbers Given an array arr[] of non-negative numbers, the task is to find GCD of all the array elements. In a previous post we find GCD of two number.Examples:Input: arr[] = [1, 2, 3]Output: 1Input: arr[] = [2, 4, 6, 8]Output: 2Using Recursive GCDThe GCD of three or more numbers equals the product of the pr 11 min read Program to find LCM of two numbers Given two positive integers a and b. Find the Least Common Multiple (LCM) of a and b.LCM of two numbers is the smallest number which can be divided by both numbers. Input : a = 10, b = 5Output : 10Explanation : 10 is the smallest number divisible by both 10 and 5Input : a = 5, b = 11Output : 55Expla 5 min read LCM of given array elements In this article, we will learn how to find the LCM of given array elements.Given an array of n numbers, find the LCM of it. Example:Input : {1, 2, 8, 3}Output : 24LCM of 1, 2, 8 and 3 is 24Input : {2, 7, 3, 9, 4}Output : 252Table of Content[Naive Approach] Iterative LCM Calculation - O(n * log(min(a 14 min read Find the other number when LCM and HCF given Given a number A and L.C.M and H.C.F. The task is to determine the other number B. Examples: Input: A = 10, Lcm = 10, Hcf = 50. Output: B = 50 Input: A = 5, Lcm = 25, Hcf = 4. Output: B = 20 Formula: A * B = LCM * HCF B = (LCM * HCF)/AExample : A = 15, B = 12 HCF = 3, LCM = 60 We can see that 3 * 60 4 min read Minimum insertions to make a Co-prime array Given an array of N elements, find the minimum number of insertions to convert the given array into a co-prime array. Print the resultant array also.Co-prime Array : An array in which every pair of adjacent elements are co-primes. i.e, gcd(a, b) = 1 . Examples : Input : A[] = {2, 7, 28}Output : 1Exp 6 min read Find the minimum possible health of the winning player Given an array health[] where health[i] is the health of the ith player in a game, any player can attack any other player in the game. The health of the player being attacked will be reduced by the amount of health the attacking player has. The task is to find the minimum possible health of the winn 4 min read Minimum squares to evenly cut a rectangle Given a rectangular sheet of length l and width w. we need to divide this sheet into square sheets such that the number of square sheets should be as minimum as possible.Examples: Input :l= 4 w=6 Output :6 We can form squares with side of 1 unit, But the number of squares will be 24, this is not min 4 min read Like