Given a set of numbers, I need to find the lowest number that multiplying it with each of the numbers in the set results in a natural number, while being bigger or equal to $N$.
For example, for the numbers $2.2$, $3$ and $4.2$, the result could be $5$, $10$, $15$, etc as they can multiply $2.2$ and $4.2$ and result in natural numbers. Then, I need the lowest one that's higher than a given number.
I'm trying to implement it as a software algorithm in an efficient way. How would I go about doing that?