For a wide class of sequences of integer domains D n ⊂ N d , n ∈ N, we prove distributional limit theorems for F(X) is a random vector with uniform distribution on D n . As a corollary, we obtain limit theorems for the greatest common divisor and least common multiple of the random setd }. This generalizes previously known limit results for D n being either a discrete cube or a discrete hyperbolic region.
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