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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?

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First find the least common multiple of the denominators. You have to multiply by that to clear the fractions, so do so. Then if $a$ is the smallest number after multiplying by the LCM, divide $N$ by $a$ and round up to the next whole number. Call that $b$. The multiplier for the original set is $b*LCM$

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Would that give me the smallest number possible? How would I go from there to finding the smallest one that's larger than N? – shesek Oct 21 '12 at 19:52
@shesek: I misread the problem, thinking you just wanted the product larger than the largest in your original set. Fixed. – Ross Millikan Oct 21 '12 at 21:59
When referring to "a is the smallest number", you mean after multiplying all the numbers by the lcm, right? – shesek Oct 21 '12 at 22:24
@shesek: It would be clearer to make it so. I was thinking that $a$ was the original smallest number, which is why I said to divide by $a * lcm$. Now it will just be $a$. I will update – Ross Millikan Oct 21 '12 at 22:28
@shesek: the LCM is taken over denominators. So if you have 3 and 7 and $N=50$, the LCM of the denominators is 1, then $b=17$ – Ross Millikan Oct 21 '12 at 23:02

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