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Java Program to Find LCM of Two Numbers

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  • Difficulty Level : Medium
  • Last Updated : 13 Jul, 2022
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LCM (i.e. Least Common Multiple) is the largest of the two stated numbers that can be divided by both the given numbers.

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Example:

LCM of 15 and 25 is 75, and LCM of 3 and 7 is 21.

Therefore, firstly find all the prime factors of both the stated numbers, then find the union of all those factors that are present in both the given numbers. And at last, return the product of elements which are in union.

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)

Note: GCD is the greatest common divisor.

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;
    }
 
    // The Driver 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

Time Complexity: O(log(min(a,b))

Auxiliary Space: O(log(min(a,b))

Similarly, you can find the LCM of any two given numbers.

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