Java Program to Find LCM of Two Numbers

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: 75

Input: 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 numbers
import java.io.*;

// Driver Class
class 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))