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Fungrim entry: c03ed9

Symbol: LCM lcm ⁣(a,b)\operatorname{lcm}\!\left(a, b\right) Least common multiple
The least common multiple function can be called either with with an arbitrary number of integer arguments or with a single finite set of integers as the argument. The current entries only deal with the case of two arguments.
Domain Codomain
aZ  and  bZa \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; b \in \mathbb{Z} lcm ⁣(a,b)Z0\operatorname{lcm}\!\left(a, b\right) \in \mathbb{Z}_{\ge 0}
SP(Z)  and  #S<#ZS \in \mathscr{P}(\mathbb{Z}) \;\mathbin{\operatorname{and}}\; \# S < \# \mathbb{Z} lcm(S)Z0\operatorname{lcm}(S) \in \mathbb{Z}_{\ge 0}
Table data: (P,Q)\left(P, Q\right) such that (P)        (Q)\left(P\right) \;\implies\; \left(Q\right)
Definitions:
Fungrim symbol Notation Short description
LCMlcm ⁣(a,b)\operatorname{lcm}\!\left(a, b\right) Least common multiple
ZZZ\mathbb{Z} Integers
ZZGreaterEqualZn\mathbb{Z}_{\ge n} Integers greater than or equal to n
PowerSetP(S)\mathscr{P}(S) Power set
Cardinality#S\# S Set cardinality
Source code for this entry:
Entry(ID("c03ed9"),
    SymbolDefinition(LCM, LCM(a, b), "Least common multiple"),
    Description("The least common multiple function can be called either with with an arbitrary number of integer arguments or with a single finite set of integers as the argument. The current entries only deal with the case of two arguments."),
    Table(TableRelation(Tuple(P, Q), Implies(P, Q)), TableHeadings(Description("Domain"), Description("Codomain")), List(Tuple(And(Element(a, ZZ), Element(b, ZZ)), Element(LCM(a, b), ZZGreaterEqual(0))), Tuple(And(Element(S, PowerSet(ZZ)), Less(Cardinality(S), Cardinality(ZZ))), Element(LCM(S), ZZGreaterEqual(0))))))

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2021-03-15 19:12:00.328586 UTC