Fungrim home page

Fungrim entry: 3605cc

(amandbm)    (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:aZandbZanddZa \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, b \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, d \in \mathbb{Z}
\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}}\, d \in \mathbb{Z}
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:
    Formula(Implies(And(Divides(a, m), Divides(b, m)), Divides(LCM(a, b), m))),
    Variables(a, b, d),
    Assumptions(And(Element(a, ZZ), Element(b, ZZ), Element(d, ZZ))))

Topics using this entry

Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2019-10-05 13:11:19.856591 UTC