Problem Statement: You are given two natural numbers A and B. Determine the natural number N such that the lowest common multiple i.e. lcm(A+N, B+N) is minimum.
If there are several values of N which yield the minimum, output the smallest one.
1 \leq A, B \leq 10^9
A = 4, B = 10
How can I approach the above problem?
I am not strong with number theory, so please give your explanations with every step explained.
It would be great if you can give me a mathematical proof of the correctness of your algorithm.