Open in App
Not now

# Print any pair of integers with sum of GCD and LCM equals to N

• Last Updated : 01 Nov, 2021

Given an integer N, the task is to print any pair of integers that have the sum of GCD and LCM equal to N.
Examples:

Input: N = 14
Output: 1, 13
Explanation
For the given pair we have GCD(1, 13) = 1 and LCM (1, 13) = 13. Sum of GCD and LCM = 1 + 13 = 14.

Input:
Output: 1 1
Explanation
For the given pair we have GCD(1, 1) = 1 and LCM (1, 1) = 1. Sum of GCD and LCM = 1 + 1 = 2.

Approach:
To solve the problem mentioned above let us consider the pair to be (1, n-1). GCD of (1, n-1) = 1 and LCM of (1, n-1) = n – 1. So the sum of GCD and LCM = 1 + (n – 1) = n. Hence the pair (1, n – 1) will be the pair which has the sum of GCD and LCM equal to N.
Below is the implementation of the above approach:

## C++

 `// C++ implementation to Print any pair of integers` `// whose summation of GCD and LCM is equal to integer N`   `#include ` `using` `namespace` `std;`   `// Function to print the required pair` `void` `printPair(``int` `n)` `{` `    ``// print the pair` `    ``cout << 1 << ``" "` `<< n - 1;` `}`   `// Driver code` `int` `main()` `{` `    ``int` `n = 14;`   `    ``printPair(n);`   `    ``return` `0;` `}`

## Java

 `// Java implementation to print any pair of integers` `// whose summation of GCD and LCM is equal to integer N` `class` `GFG{`   `// Function to print the required pair` `static` `void` `printPair(``int` `n)` `{` `    ``// Print the pair` `    ``System.out.print(``1` `+ ``" "` `+ (n - ``1``));` `}`   `// Driver code` `public` `static` `void` `main(String[] args)` `{` `    ``int` `n = ``14``;` `    ``printPair(n);` `}` `}`   `// This code is contributed by gauravrajput1`

## Python3

 `# Python3 implementation to print any ` `# pair of integers whose summation of` `# GCD and LCM is equal to integer N `   `# Function to print the required pair ` `def` `printPair(n): `   `    ``# Print the pair ` `    ``print``(``"1"``, end ``=` `" "``)` `    ``print``(n ``-` `1``)`   `# Driver code ` `n ``=` `14` `printPair(n)`   `# This code is contributed by PratikBasu`

## C#

 `// C# implementation to print any pair` `// of integers whose summation of` `// GCD and LCM is equal to integer N` `using` `System;`   `public` `class` `GFG{`   `// Function to print the required pair` `static` `void` `printPair(``int` `n)` `{` `    `  `    ``// Print the pair` `    ``Console.Write(1 + ``" "` `+ (n - 1));` `}`   `// Driver code` `public` `static` `void` `Main(String[] args)` `{` `    ``int` `n = 14;` `    ``printPair(n);` `}` `}`   `// This code is contributed by Princi Singh`

## Javascript

 ``

Output:

`1 13`

Time Complexity:O(1)

Auxiliary Space:O(1)

My Personal Notes arrow_drop_up
Related Articles