Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On certain sums concerning the gcd's and lcm's of $k$ positive integers   We use elementary arguments to prove results on the order of magnitude of
certain sums concerning the gcd's and lcm's of $k$ positive integers, where
$k\ge 2$ is fixed. We refine and generalize an asymptotic formula of
Bordell\`{e}s (2007), and extend certain related results of Hilberdink and
T\'oth (2016). We also formulate some conjectures and open problems.

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The categories of this paper are: gr-qc
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The categories of this paper are: atom-ph
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The categories of this paper are: eess
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The categories of this paper are: cs
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The categories of this paper are: hep-th
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The categories of this paper are: funct-an
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The categories of this paper are: nucl-th
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The categories of this paper are: q-bio
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The categories of this paper are: bayes-an
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The categories of this paper are: ao-sci
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The categories of this paper are: cmp-lg
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The categories of this paper are: plasm-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: supr-con
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The categories of this paper are: astro-ph