# Maximum LCM among all pairs (i, j) of first N natural numbers

Given a positive integer **N > 1**, the task is to find the maximum LCM among all the pairs **(i, j)** such that **i < j ≤ N**.**Examples:**

Input:N = 3Output:6

LCM(1, 2) = 2

LCM(1, 3) = 3

LCM(2, 3) = 6Input:N = 4Output:12

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**Approach:** Since the LCM of two consecutive elements is equal to their multiples then it is obvious that the maximum LCM will be of the pair **(N, N – 1)** i.e. **(N * (N – 1))**.

Below is the implementation of the above approach:

## C++

`// C++ implementation of the approach` `#include <bits/stdc++.h>` `using` `namespace` `std;` `// Function to return the maximum LCM` `// among all the pairs(i, j) of` `// first n natural numbers` `int` `maxLCM(` `int` `n)` `{` ` ` `return` `(n * (n - 1));` `}` `// Driver code` `int` `main()` `{` ` ` `int` `n = 3;` ` ` `cout << maxLCM(n);` ` ` `return` `0;` `}` |

## Java

`// Java implementation of the approach` `class` `GFG` `{` ` ` `// Function to return the maximum LCM` `// among all the pairs(i, j) of` `// first n natural numbers` `static` `int` `maxLCM(` `int` `n)` `{` ` ` `return` `(n * (n - ` `1` `));` `}` `// Driver code` `public` `static` `void` `main(String[] args)` `{` ` ` `int` `n = ` `3` `;` ` ` `System.out.println(maxLCM(n));` `}` `}` `// This code is contributed by Code_Mech` |

## Python3

`# Python3 implementation of the approach` `# Function to return the maximum LCM` `# among all the pairs(i, j) of` `# first n natural numbers` `def` `maxLCM(n) :` ` ` `return` `(n ` `*` `(n ` `-` `1` `));` `# Driver code` `if` `__name__ ` `=` `=` `"__main__"` `:` ` ` `n ` `=` `3` `;` ` ` `print` `(maxLCM(n));` `# This code is contributed by AnkitRai01` |

## C#

`// C# implementation of the approach` `using` `System;` ` ` `class` `GFG` `{` ` ` `// Function to return the maximum LCM` `// among all the pairs(i, j) of` `// first n natural numbers` `static` `int` `maxLCM(` `int` `n)` `{` ` ` `return` `(n * (n - 1));` `}` `// Driver code` `public` `static` `void` `Main(String[] args)` `{` ` ` `int` `n = 3;` ` ` `Console.WriteLine(maxLCM(n));` `}` `}` `// This code is contributed by Rajput-Ji` |

## Javascript

`<script>` `// Javascript implementation of the approach` `// Function to return the maximum LCM` `// among all the pairs(i, j) of` `// first n natural numbers` `function` `maxLCM(n)` `{` ` ` `return` `(n * (n - 1));` `}` `// Driver code` `var` `n = 3;` `document.write(maxLCM(n));` `</script>` |

**Output:**

6

**Time Complexity:** O(1)