Fungrim home page

Fungrim entry: 5d03d2

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

a \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, b \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, d \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("5d03d2"),
    Formula(Implies(Or(Divides(d, a), Divides(d, b)), Divides(d, LCM(a, b)))),
    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.

2019-06-18 07:49:59.356594 UTC