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

• Last Updated : 10 Mar, 2022

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

Input: N = 3
Output:
LCM(1, 2) = 2
LCM(1, 3) = 3
LCM(2, 3) = 6
Input: N = 4
Output: 12

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`

## Javascript

 ``

Output:

`6`

Time Complexity: O(1)

Auxiliary Space: O(1)

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