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Fungrim entry: dc0823

lcm⁡ ⁣(a,b)=lcm⁡ ⁣(−a,b)=lcm⁡ ⁣(a,−b)=lcm⁡ ⁣(−a,−b)\operatorname{lcm}\!\left(a, b\right) = \operatorname{lcm}\!\left(-a, b\right) = \operatorname{lcm}\!\left(a, -b\right) = \operatorname{lcm}\!\left(-a, -b\right)
Assumptions:a∈Z  and⁡  b∈Za \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; b \in \mathbb{Z}
TeX:
\operatorname{lcm}\!\left(a, b\right) = \operatorname{lcm}\!\left(-a, b\right) = \operatorname{lcm}\!\left(a, -b\right) = \operatorname{lcm}\!\left(-a, -b\right)

a \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; b \in \mathbb{Z}
Definitions:
Fungrim symbol Notation Short description
LCMlcm⁡ ⁣(a,b)\operatorname{lcm}\!\left(a, b\right) Least common multiple
ZZZ\mathbb{Z} Integers
Source code for this entry:
Entry(ID("dc0823"),
    Formula(Equal(LCM(a, b), LCM(Neg(a), b), LCM(a, Neg(b)), LCM(Neg(a), Neg(b)))),
    Variables(a, b),
    Assumptions(And(Element(a, ZZ), Element(b, ZZ))))

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2021-03-15 19:12:00.328586 UTC