Fungrim entry: 250a45

\operatorname{lcm}\!\left(r, s\right) = \left|r s\right|

Assumptions:

r \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; s \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; \gcd\!\left(r, s\right) = 1

TeX:

\operatorname{lcm}\!\left(r, s\right) = \left|r s\right|

r \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; s \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; \gcd\!\left(r, s\right) = 1

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("250a45"),
    Formula(Equal(LCM(r, s), Abs(Mul(r, s)))),
    Variables(r, s),
    Assumptions(And(Element(r, ZZ), Element(s, ZZ), Equal(GCD(r, s), 1))))

Topics using this entry

Greatest common divisor

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