# Fungrim entry: fbe121

$\operatorname{lcm}\!\left(r s, c\right) = \frac{\operatorname{lcm}\!\left(r, c\right) \operatorname{lcm}\!\left(s, c\right)}{\left|c\right|}$
Assumptions:$r \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; s \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; c \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; \gcd\!\left(r, s\right) = 1 \;\mathbin{\operatorname{and}}\; c \ne 0$
TeX:
\operatorname{lcm}\!\left(r s, c\right) = \frac{\operatorname{lcm}\!\left(r, c\right) \operatorname{lcm}\!\left(s, c\right)}{\left|c\right|}

r \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; s \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; c \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; \gcd\!\left(r, s\right) = 1 \;\mathbin{\operatorname{and}}\; c \ne 0
Definitions:
Fungrim symbol Notation Short description
LCM$\operatorname{lcm}\!\left(a, b\right)$ Least common multiple
Abs$\left|z\right|$ Absolute value
ZZ$\mathbb{Z}$ Integers
GCD$\gcd\!\left(a, b\right)$ Greatest common divisor
Source code for this entry:
Entry(ID("fbe121"),
Formula(Equal(LCM(Mul(r, s), c), Div(Mul(LCM(r, c), LCM(s, c)), Abs(c)))),
Variables(r, s, c),
Assumptions(And(Element(r, ZZ), Element(s, ZZ), Element(c, ZZ), Equal(GCD(r, s), 1), NotEqual(c, 0))))

## 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