Fungrim entry: 4d3127

\gcd\!\left(a, b\right) \operatorname{lcm}\!\left(a, b\right) = \left|a b\right|

Assumptions:

a \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, b \in \mathbb{Z}

TeX:

\gcd\!\left(a, b\right) \operatorname{lcm}\!\left(a, b\right) = \left|a b\right|

a \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, b \in \mathbb{Z}

Definitions:

Fungrim symbol	Notation	Short description
`GCD`	$\gcd\!\left(n, k\right)$	Greatest common divisor
`LCM`	$\operatorname{lcm}\!\left(a, b\right)$	Least common multiple
`Abs`	$\left\|z\right\|$	Absolute value
`ZZ`	$\mathbb{Z}$	Integers

Source code for this entry:

Entry(ID("4d3127"),
    Formula(Equal(Mul(GCD(a, b), LCM(a, b)), Abs(Mul(a, b)))),
    Variables(a, b),
    Assumptions(And(Element(a, ZZ), Element(b, ZZ))))

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.

2019-06-18 07:49:59.356594 UTC