Discover the quantity N, the place (N+X) divisible by Y and (N-Y) divisible by X

Given two numbers X and Y. the duty is to search out the quantity N (N ≤ 10^18) which satisfies these two situations:

• (N + X) is divisible by Y
• (N – Y) is divisible by X

Examples:

Enter: X = 18, Y = 42
Output:780

Enter: X = 100, Y = 200
Output: 500

Strategy: The issue could be solved primarily based on the next concept:

We will implement the easy math idea of the quantity system.

• N + X = Y    …………(i)
• N – Y = X     …………(ii)

Normalizes the equation we are able to get N could also be equal to (X*Y – X + Y). Additionally, it’s satisfying these two situations. So, the reply is (X * Y – X + Y).

Beneath is the implementation of the above method:

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