# 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 = 3
Output: 6
LCM(1, 2) = 2
LCM(1, 3) = 3
LCM(2, 3) = 6

Input: N = 4
Output: 12

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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 ` `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 `

Output:

```6
```

Time Complexity: O(1)

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