# Program to find LCM of two numbers

LCM (Least Common Multiple) of two numbers is the smallest number which can be divided by both numbers.

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For example, LCM of 15 and 20 is 60, and LCM of 5 and 7 is 35.

A **simple solution** is to find all prime factors of both numbers, then find union of all factors present in both numbers. Finally, return the product of elements in union.

An **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.

Below is the implementation of the above idea:

## C++

`// C++ program to find LCM of two numbers` `#include <iostream>` `using` `namespace` `std;` `// Recursive function to return gcd of a and b` `long` `long` `gcd(` `long` `long` `int` `a, ` `long` `long` `int` `b)` `{` ` ` `if` `(b == 0)` ` ` `return` `a;` ` ` `return` `gcd(b, a % b);` `}` `// Function to return LCM of two numbers` `long` `long` `lcm(` `int` `a, ` `int` `b)` `{` ` ` `return` `(a / gcd(a, b)) * b;` `}` ` ` `// Driver program to test above function` `int` `main()` `{` ` ` `int` `a = 15, b = 20;` ` ` `cout <<` `"LCM of "` `<< a << ` `" and "` ` ` `<< b << ` `" is "` `<< lcm(a, b);` ` ` `return` `0;` `}` |

## C

`// C program to find LCM of two numbers` `#include <stdio.h>` `// Recursive function to return gcd of a and b` `int` `gcd(` `int` `a, ` `int` `b)` `{` ` ` `if` `(a == 0)` ` ` `return` `b;` ` ` `return` `gcd(b % a, a);` `}` `// Function to return LCM of two numbers` `int` `lcm(` `int` `a, ` `int` `b)` `{` ` ` `return` `(a / gcd(a, b)) * b;` `}` `// Driver program to test above function` `int` `main()` `{` ` ` `int` `a = 15, b = 20;` ` ` `printf` `(` `"LCM of %d and %d is %d "` `, a, b, lcm(a, b));` ` ` `return` `0;` `}` |

## Java

`// Java program to find LCM of two numbers.` `class` `Test` `{` ` ` `// Recursive method to return gcd of a and b` ` ` `static` `int` `gcd(` `int` `a, ` `int` `b)` ` ` `{` ` ` `if` `(a == ` `0` `)` ` ` `return` `b;` ` ` `return` `gcd(b % a, a);` ` ` `}` ` ` ` ` `// method to return LCM of two numbers` ` ` `static` `int` `lcm(` `int` `a, ` `int` `b)` ` ` `{` ` ` `return` `(a / gcd(a, b)) * b;` ` ` `}` ` ` ` ` `// Driver method` ` ` `public` `static` `void` `main(String[] args)` ` ` `{` ` ` `int` `a = ` `15` `, b = ` `20` `;` ` ` `System.out.println(` `"LCM of "` `+ a +` ` ` `" and "` `+ b +` ` ` `" is "` `+ lcm(a, b));` ` ` `}` `}` |

## Python3

`# Python program to find LCM of two numbers` `# Recursive function to return gcd of a and b` `def` `gcd(a,b):` ` ` `if` `a ` `=` `=` `0` `:` ` ` `return` `b` ` ` `return` `gcd(b ` `%` `a, a)` `# Function to return LCM of two numbers` `def` `lcm(a,b):` ` ` `return` `(a ` `/` `gcd(a,b))` `*` `b` `# Driver program to test above function` `a ` `=` `15` `b ` `=` `20` `print` `(` `'LCM of'` `, a, ` `'and'` `, b, ` `'is'` `, lcm(a, b))` `# This code is contributed by Danish Raza` |

## C#

`// C# program to find LCM` `// of two numbers.` `using` `System;` `class` `GFG {` ` ` ` ` `// Recursive method to` ` ` `// return gcd of a and b` ` ` `static` `int` `gcd(` `int` `a, ` `int` `b)` ` ` `{` ` ` `if` `(a == 0)` ` ` `return` `b;` ` ` `return` `gcd(b % a, a);` ` ` `}` ` ` ` ` `// method to return` ` ` `// LCM of two numbers` ` ` `static` `int` `lcm(` `int` `a, ` `int` `b)` ` ` `{` ` ` `return` `(a / gcd(a, b)) * b;` ` ` `}` ` ` ` ` `// Driver method` ` ` `public` `static` `void` `Main()` ` ` `{` ` ` `int` `a = 15, b = 20;` ` ` `Console.WriteLine(` `"LCM of "` `+ a +` ` ` `" and "` `+ b + ` `" is "` `+ lcm(a, b));` ` ` `}` `}` `// This code is contributed by anuj_67.` |

## PHP

`<?php` `// PHP program to find LCM of two numbers` `// Recursive function to` `// return gcd of a and b` `function` `gcd( ` `$a` `, ` `$b` `)` `{` ` ` `if` `(` `$a` `== 0)` ` ` `return` `$b` `;` ` ` `return` `gcd(` `$b` `% ` `$a` `, ` `$a` `);` `}` `// Function to return LCM` `// of two numbers` `function` `lcm( ` `$a` `, ` `$b` `)` `{` ` ` `return` `(` `$a` `/ gcd(` `$a` `, ` `$b` `)) * ` `$b` `;` `}` ` ` `// Driver Code` ` ` `$a` `= 15;` ` ` `$b` `= 20;` ` ` `echo` `"LCM of "` `,` `$a` `, ` `" and "` ` ` `,` `$b` `, ` `" is "` `, lcm(` `$a` `, ` `$b` `);` `// This code is contributed by anuj_67.` `?>` |

## Javascript

`<script>` `// Javascript program to find LCM of two numbers` `// Recursive function to return gcd of a and b` `function` `gcd(a, b)` `{` `if` `(b == 0)` ` ` `return` `a;` `return` `gcd(b, a % b);` `}` `// Function to return LCM of two numbers` `function` `lcm(a, b)` `{` ` ` `return` `(a / gcd(a, b)) * b;` `}` `// Driver program to test above function` ` ` ` ` `let a = 15, b = 20;` ` ` `document.write(` `"LCM of "` `+ a + ` `" and "` ` ` `+ b + ` `" is "` `+ lcm(a, b));` ` ` `// This code is contributed by Mayank Tyagi` `</script>` |

**Output**

LCM of 15 and 20 is 60

**Time Complexity: **O(log(max(a,b))

**Auxiliary Space: **O(log(max(a,b))

https://youtu.be/anSfYgbo694

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