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.
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:
- Select the value of x as L and compute the value of y as 2*x
- Check if y is less than R or not.
- If y is less than R then print the pair (x, y)
- Else print “-1”
Below is the implementation of the above approach:
X = 13 Y = 26
Time Complexity: O(1)
Auxiliary Space: O(1)
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