Fungrim entry: 5d03d2

$\left(d \mid a \,\mathbin{\operatorname{or}}\, d \mid b\right) \implies \left(d \mid \operatorname{lcm}\!\left(a, b\right)\right)$
Assumptions:$a \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, b \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, d \in \mathbb{Z}$
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
LCM$\operatorname{lcm}\!\left(a, b\right)$ Least common multiple
ZZ$\mathbb{Z}$ 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.

2019-08-21 11:44:15.926409 UTC