# Fungrim entry: 6572c5

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

a \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; b \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; a \ne 0 \;\mathbin{\operatorname{and}}\; b \ne 0
Definitions:
Fungrim symbol Notation Short description
GCD$\gcd\!\left(a, b\right)$ Greatest common divisor
Abs$\left|z\right|$ Absolute value
LCM$\operatorname{lcm}\!\left(a, b\right)$ Least common multiple
ZZ$\mathbb{Z}$ Integers
Source code for this entry:
Entry(ID("6572c5"),
Formula(Equal(GCD(a, b), Div(Abs(Mul(a, b)), LCM(a, b)))),
Variables(a, b),
Assumptions(And(Element(a, ZZ), Element(b, ZZ), NotEqual(a, 0), NotEqual(b, 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