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Fungrim entry: 3605cc

(a∣m  and⁡  b∣m)    ⟹    (lcm⁡ ⁣(a,b)∣m)\left(a \mid m \;\mathbin{\operatorname{and}}\; b \mid m\right) \;\implies\; \left(\operatorname{lcm}\!\left(a, b\right) \mid m\right)
Assumptions:a∈Z  and⁡  b∈Z  and⁡  m∈Za \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; b \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; m \in \mathbb{Z}
TeX:
\left(a \mid m \;\mathbin{\operatorname{and}}\; b \mid m\right) \;\implies\; \left(\operatorname{lcm}\!\left(a, b\right) \mid m\right)

a \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; b \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; m \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("3605cc"),
    Formula(Implies(And(Divides(a, m), Divides(b, m)), Divides(LCM(a, b), m))),
    Variables(a, b, m),
    Assumptions(And(Element(a, ZZ), Element(b, ZZ), Element(m, ZZ))))

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2021-03-15 19:12:00.328586 UTC