# Fungrim entry: 927e6e

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

a \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, b \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, \left(a \ne 0 \,\mathbin{\operatorname{or}}\, b \ne 0\right)
Definitions:
Fungrim symbol Notation Short description
LCM$\operatorname{lcm}\!\left(a, b\right)$ Least common multiple
Abs$\left|z\right|$ Absolute value
GCD$\gcd\!\left(a, b\right)$ Greatest common divisor
ZZ$\mathbb{Z}$ Integers
Source code for this entry:
Entry(ID("927e6e"),
Formula(Equal(LCM(a, b), Div(Abs(Mul(a, b)), GCD(a, b)))),
Variables(a, b),
Assumptions(And(Element(a, ZZ), Element(b, ZZ), Or(Unequal(a, 0), Unequal(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.

2019-08-21 11:44:15.926409 UTC