Given two numbers L and R, the task is to find two distinct minimum positive integers X and Y such that whose LCM lies in the range [L, R]. If there doesn’t exist any value of X and Y then print “-1”.
Input: L = 3, R = 8
Output: x = 3, y=6
LCM of 3 and 6 is 6 which is in range 3, 8
Input: L = 88, R = 90
Minimum possible x and y are 88 and 176 respectively, but 176 is greater than 90.
Approach: The idea is to choose the value of X and Y in such a way that their LCM lies in the given range [L, R]. Below are the steps:
- For the minimum value of X choose L as the minimum value as this is the minimum value in the given range.
- Now for the value of Y choose 2*L as this is the minimum value of Y whose LCM is L.
- Now if the above two values of X and Y lie in the range [L, R], then this is required pair of integers with minimum possible values of X and Y.
- Otherwise, print “-1” as there doesn’t exist any other pair.
Below is the implementation of the above approach:
Time Complexity: O(1)
Auxiliary Space: O(1)
- Sum of LCM(1, n), LCM(2, n), LCM(3, n), ... , LCM(n, n)
- Generate a pair of integers from a range [L, R] whose LCM also lies within the range
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Improved By : sanjoy_62