Fungrim entry: 1277f6

\gcd\!\left(a, b\right) \mid \operatorname{lcm}\!\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{and}}\, b \ne 0\right)

TeX:

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

a \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, b \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, \left(a \ne 0 \,\mathbin{\operatorname{and}}\, b \ne 0\right)

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
`ZZ`	$\mathbb{Z}$	Integers

Source code for this entry:

Entry(ID("1277f6"),
    Formula(Divides(GCD(a, b), LCM(a, b))),
    Variables(a, b),
    Assumptions(And(Element(a, ZZ), Element(b, ZZ), And(Unequal(a, 0), Unequal(b, 0)))))

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