# 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. In this article, we will write a program to find the LCM in Java

## Java Program to Find the LCM of Two Numbers

The easiest approach for finding the LCM is to Check the factors and then find the Union of all factors to get the result.

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

```

## Using Greatest Common Divisor

Below given formula for finding the LCM of two numbers â€˜uâ€™ and â€˜vâ€™ 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.

## 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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