Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On property of least common multiple to be a $D$-magic number   Least common multiple ($lcm$) has been shown to posses the property of
$D$-magic number, that is, its least significant digit $0$ does not change when
the number is transferred into all other numbering systems with smaller bases.
The number $lcm + 1$ preserves this property as well.

13
The categories of this paper are: quant-ph
24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con
1
The categories of this paper are: cs
4
The categories of this paper are: cond-mat
33
The categories of this paper are: plasm-ph
32
The categories of this paper are: atom-ph
28
The categories of this paper are: alg-geom
16
The categories of this paper are: stat
17
The categories of this paper are: q-fin
6
The categories of this paper are: astro-ph
29
The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
18
The categories of this paper are: econ
27
The categories of this paper are: comp-gas