# Generate a pair of integers from a range [L, R] whose LCM also lies within the range

Given two integers L and R, the task is to find a pair of integers from the range [L, R] having LCM within the range [L, R] as well. If no such pair can be obtained, then print -1. If multiple pairs exist, print any one of them.

Examples:

Input: L = 13, R = 69
Output: X =13, Y = 26
Explanation: LCM(x, y) = 26 which satisfies the conditions L ≤ x < y ≤ R and L <= LCM(x, y) <= R

Input: L = 1, R = 665
Output: X = 1, Y = 2

Naive Approach: The simplest approach is to generate every pair between L and R and compute their LCM. Print a pair having LCM between the range L and R. If no pair is found to have LCM in the given range, print “-1”.

Time Complexity: O(N)
Auxiliary Space: O(1)

Efficient Approach: The problem can be solved by using the Greedy technique based on the observation that LCM(x, y) is at least equal to 2*x which is LCM of (x, 2*x). Below are the steps to implement the approach:

1. Select the value of x as L and compute the value of y as 2*x
2. Check if y is less than R or not.
3. If y is less than R then print the pair (x, y)
4. Else print “-1”

Below is the implementation of the above approach:

 `// C++ implementation of the above approach` `#include ` `using` `namespace` `std;`   `void` `lcmpair(``int` `l, ``int` `r)` `{` `    ``int` `x, y;` `    ``x = l;` `    ``y = 2 * l;`   `    ``// Checking if any pair is possible` `    ``// or not in range(l, r)` `    ``if` `(y > r) {`   `        ``// If not possible print(-1)` `        ``cout << ``"-1\n"``;` `    ``}` `    ``else` `{`   `        ``// Print LCM pair` `        ``cout << ``"X = "` `<< x << ``" Y = "` `             ``<< y << ``"\n"``;` `    ``}` `}`   `// Driver code` `int` `main()` `{` `    ``int` `l = 13, r = 69;`   `    ``// Function call` `    ``lcmpair(l, r);` `    ``return` `0;` `}`

 `// Java implementation of the above approach` `import` `java.util.*;`   `class` `GFG{`   `static` `void` `lcmpair(``int` `l, ``int` `r)` `{` `    ``int` `x, y;` `    ``x = l;` `    ``y = ``2` `* l;`   `    ``// Checking if any pair is possible` `    ``// or not in range(l, r)` `    ``if` `(y > r) ` `    ``{` `        `  `        ``// If not possible print(-1)` `        ``System.out.print(``"-1\n"``);` `    ``}` `    ``else` `    ``{` `        `  `        ``// Print LCM pair` `        ``System.out.print(``"X = "` `+ x + ` `                        ``" Y = "` `+ y + ``"\n"``);` `    ``}` `}`   `// Driver code` `public` `static` `void` `main(String[] args)` `{` `    ``int` `l = ``13``, r = ``69``;`   `    ``// Function call` `    ``lcmpair(l, r);` `}` `}`   `// This code is contributed by 29AjayKumar `

 `# Python3 implementation of the above approach ` `def` `lcmpair(l, r):`   `    ``x ``=` `l` `    ``y ``=` `2` `*` `l`   `    ``# Checking if any pair is possible` `    ``# or not in range(l, r)` `    ``if``(y > r):`   `        ``# If not possible print(-1)` `        ``print``(``-``1``)` `    ``else``:` `        `  `        ``# Print LCM pair` `        ``print``(``"X = {} Y = {}"``.``format``(x, y))`   `# Driver Code` `l ``=` `13` `r ``=` `69`   `# Function call` `lcmpair(l, r)`   `# This code is contributed by Shivam Singh`

 `// C# implementation of the above approach` `using` `System;` `class` `GFG{`   `static` `void` `lcmpair(``int` `l, ``int` `r)` `{` `    ``int` `x, y;` `    ``x = l;` `    ``y = 2 * l;`   `    ``// Checking if any pair is possible` `    ``// or not in range(l, r)` `    ``if` `(y > r) ` `    ``{        ` `        ``// If not possible print(-1)` `        ``Console.Write(``"-1\n"``);` `    ``}` `    ``else` `    ``{        ` `        ``// Print LCM pair` `        ``Console.Write(``"X = "` `+ x + ` `                      ``" Y = "` `+ y + ``"\n"``);` `    ``}` `}`   `// Driver code` `public` `static` `void` `Main(String[] args)` `{` `    ``int` `l = 13, r = 69;`   `    ``// Function call` `    ``lcmpair(l, r);` `}` `}`   `// This code is contributed by shikhasingrajput`

Output:
```X = 13 Y = 26

```

Time Complexity: O(1)
Auxiliary Space: O(1)

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