For a given set of numbers, I need to find the lowest common divisor that's higher than a given number, N. Is there a way to do that?
Find the lowest common divisor greater than N?
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elementary-number-theory
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0Do you mean the least common *multiple* that is greater than $N$? – 2012-10-21
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0No. I do mean a _divisor_. – 2012-10-21
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1@shesek Any common divisor divides the gcd and every divisor of gcd is a common divisor. Hence, what you are after is $$\min \{d| \gcd(x_1,x_2,\ldots,x_k): d > N\}$$ Is this what you are after and am I interpreting your question correctly? – 2012-10-21
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3I’d find the gcd $d$ of the set of numbers. If I could easily find its prime factorization, I’d do so, and from that I’d find the smallest subproduct bigger than $N$. – 2012-10-21
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0@Marvis I think you are, tho I'm not quite sure what that formula means (not much of a math background, I'm a programmer). Can you elaborate? – 2012-10-21
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0@BrianM.Scott So I would generate all the possible subproducts of the prime factors, than find the lowest one bigger than N? Or is there a better way to do that? I'm trying to implement as an software algorithm, in the most efficient way possible. – 2012-10-21
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1If I were programming it, I don’t think that I’d bother with the prime factors: factorization tends to be difficult. You might find that a simple search from $N+1$ to $d$, testing each number to see whether it divides $d$ and picking the first hit, is the way to go. – 2012-10-21
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0Actually, I think I found another way to accomplish what I'm trying to implement in my software. I asked at http://math.stackexchange.com/q/218210/45513. Thanks for all the help! – 2012-10-21