Given a number , find the number of distinct integers obtained by lcm(X, N)/X where X can be any positive number.
Input: N = 2 Output: 2 if X is 1, then lcm(1, 2)/1 is 2/1=2. if X is 2, then lcm(2, 2)/2 is 2/2=1. For any X greater than 2 we cannot obtain a distinct integer. Input: N = 3 Output: 2
It is known that lcm(x, y) = x*y/gcd(x, y).
lcm(X, N) = X*N/gcd(X, N) or, lcm(X, N)/X = N/gcd(X, N)
So only the distinct factors of can be the distinct integers possible. Hence count the number of distinct factors of N including 1 and N itself, which is the required answer.
Below is the implementation of the above approach:
Time Complexity: O(sqrt(n))
- Total distinct pairs from two arrays such that second number can be obtained by inverting bits of first
- Maximum number of distinct positive integers that can be used to represent N
- Check whether a number can be represented as sum of K distinct positive integers
- Count of integers obtained by replacing ? in the given string that give remainder 5 when divided by 13
- Find N distinct integers with sum N
- Find N distinct integers with zero sum
- Find K distinct positive odd integers with sum N
- Find any K distinct odd integers such that their sum is equal to N
- Represent (2 / N) as the sum of three distinct positive integers of the form (1 / m)
- Find distinct integers for a triplet with given product
- Check if the sum of distinct digits of two integers are equal
- Integers from the range that are composed of a single distinct digit
- Generate permutation of 1 to N such that absolute difference of consecutive numbers give K distinct integers
- Find the final number obtained after performing the given operation
- Find the number obtained after concatenation of binary representation of M and N
If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to email@example.com. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.