Fungrim symbol: LCM

Symbol: LCM —

\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
$a \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; b \in \mathbb{Z}$	$\operatorname{lcm}\!\left(a, b\right) \in \mathbb{Z}_{\ge 0}$
$S \in \mathscr{P}(\mathbb{Z}) \;\mathbin{\operatorname{and}}\; \# S < \# \mathbb{Z}$	$\operatorname{lcm}(S) \in \mathbb{Z}_{\ge 0}$

Table data:

\left(P, Q\right)

such that

\left(P\right) \;\implies\; \left(Q\right)

Definitions:

Fungrim symbol	Notation	Short description
`LCM`	$\operatorname{lcm}\!\left(a, b\right)$	Least common multiple
`ZZ`	$\mathbb{Z}$	Integers
`ZZGreaterEqual`	$\mathbb{Z}_{\ge n}$	Integers greater than or equal to n
`PowerSet`	$\mathscr{P}(S)$	Power set
`Cardinality`	$\# S$	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))))))

Topics using this symbol

The symbol LCM appears in 3 topics:

Greatest common divisor (in 37 entries)
Totient function (in 2 entries)
Landau's function (in 1 entries)

Entries using this symbol

The symbol LCM appears in 40 entries: