LCM (i.e. Least Common Multiple) is the largest of the two stated numbers that can be divided by both the given numbers.
Example for LCM of Two Numbers
Input: LCM( 15 and 25)
Output: 75Input: LCM( 3 and 7 )
Output: 21
Methods to Find LCM
There are certain methods to Find the LCM of two numbers as mentioned below:
- Using if statement
- Using GCD
1. Using if statement to Find the LCM of Two Numbers
Using if is a really simple method and also can be said brute force method.
Below is the implementation of the above method:
Java
// Java Program to find// the LCM of two numbersimport java.io.*;// Driver Classclass GFG { // main function public static void main(String[] args) { // Numbers int a = 15, b = 25; // Checking for the smaller // Number between them int ans = (a > b) ? a : b; // Checking for a smallest number that // can de divided by both numbers while (true) { if (ans % a == 0 && ans % b == 0) break; ans++; } // Printing the Result System.out.println("LCM of " + a + " and " + b + " : " + ans); }} |
Output
LCM of 15 and 25 : 75
2. Using Greatest Common Divisor
Below given formula for finding the LCM of two numbers ‘u’ and ‘v’ gives an efficient solution.
u x v = LCM(u, v) * GCD (u, v) LCM(u, v) = (u x v) / GCD(u, v)
Here, GCD is the greatest common divisor.
Below is the implementation of the above method:
Java
// Java program to find LCM// of two numbers.class gfg { // Gcd of u and v // using recursive method static int GCD(int u, int v) { if (u == 0) return v; return GCD(v % u, u); } // LCM of two numbers static int LCM(int u, int v) { return (u / GCD(u, v)) * v; } // main method public static void main(String[] args) { int u = 25, v = 15; System.out.println("LCM of " + u + " and " + v + " is " + LCM(u, v)); }} |
Output
LCM of 25 and 15 is 75
Complexity of the above method:
Time Complexity: O(log(min(a,b))
Auxiliary Space: O(log(min(a,b))
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