# Fungrim entry: c4a892

$\operatorname{lcm}\!\left(a, \gcd\!\left(b, c\right)\right) = \gcd\!\left(\operatorname{lcm}\!\left(a, b\right), \operatorname{lcm}\!\left(a, c\right)\right)$
Assumptions:$a \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; b \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; c \in \mathbb{Z}$
TeX:
\operatorname{lcm}\!\left(a, \gcd\!\left(b, c\right)\right) = \gcd\!\left(\operatorname{lcm}\!\left(a, b\right), \operatorname{lcm}\!\left(a, c\right)\right)

a \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; b \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; c \in \mathbb{Z}
Definitions:
Fungrim symbol Notation Short description
LCM$\operatorname{lcm}\!\left(a, b\right)$ Least common multiple
GCD$\gcd\!\left(a, b\right)$ Greatest common divisor
ZZ$\mathbb{Z}$ Integers
Source code for this entry:
Entry(ID("c4a892"),
Formula(Equal(LCM(a, GCD(b, c)), GCD(LCM(a, b), LCM(a, c)))),
Variables(a, b, c),
Assumptions(And(Element(a, ZZ), Element(b, ZZ), Element(c, ZZ))))

## Topics using this entry

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

2021-03-15 19:12:00.328586 UTC