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 ≤ 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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