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Fungrim entry: 805c7a

lcm ⁣(a,b)=min{m:mZ1andamandbm}\operatorname{lcm}\!\left(a, b\right) = \min \left\{ m : m \in \mathbb{Z}_{\ge 1} \,\mathbin{\operatorname{and}}\, a \mid m \,\mathbin{\operatorname{and}}\, b \mid m \right\}
Assumptions:aZ{0}andbZ{0}a \in \mathbb{Z} \setminus \left\{0\right\} \,\mathbin{\operatorname{and}}\, b \in \mathbb{Z} \setminus \left\{0\right\}
TeX:
\operatorname{lcm}\!\left(a, b\right) = \min \left\{ m : m \in \mathbb{Z}_{\ge 1} \,\mathbin{\operatorname{and}}\, a \mid m \,\mathbin{\operatorname{and}}\, b \mid m \right\}

a \in \mathbb{Z} \setminus \left\{0\right\} \,\mathbin{\operatorname{and}}\, b \in \mathbb{Z} \setminus \left\{0\right\}
Definitions:
Fungrim symbol Notation Short description
LCMlcm ⁣(a,b)\operatorname{lcm}\!\left(a, b\right) Least common multiple
MinimumminP(x)f ⁣(x)\mathop{\min}\limits_{P\left(x\right)} f\!\left(x\right) Minimum value of a set or function
SetBuilder{f ⁣(x):P ⁣(x)}\left\{ f\!\left(x\right) : P\!\left(x\right) \right\} Set comprehension
ZZGreaterEqualZn\mathbb{Z}_{\ge n} Integers greater than or equal to n
ZZZ\mathbb{Z} Integers
Source code for this entry:
Entry(ID("805c7a"),
    Formula(Equal(LCM(a, b), Minimum(SetBuilder(m, m, And(Element(m, ZZGreaterEqual(1)), Divides(a, m), Divides(b, m)))))),
    Variables(a, b),
    Assumptions(And(Element(a, SetMinus(ZZ, Set(0))), Element(b, SetMinus(ZZ, Set(0))))))

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2019-08-21 11:44:15.926409 UTC