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Fungrim entry: 1d1653

gcd ⁣(a,lcm ⁣(a,b))=a\gcd\!\left(a, \operatorname{lcm}\!\left(a, b\right)\right) = \left|a\right|
Assumptions:aZandbZa \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, b \in \mathbb{Z}
TeX:
\gcd\!\left(a, \operatorname{lcm}\!\left(a, b\right)\right) = \left|a\right|

a \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, b \in \mathbb{Z}
Definitions:
Fungrim symbol Notation Short description
GCDgcd ⁣(n,k)\gcd\!\left(n, k\right) Greatest common divisor
LCMlcm ⁣(a,b)\operatorname{lcm}\!\left(a, b\right) Least common multiple
Absz\left|z\right| Absolute value
ZZZ\mathbb{Z} Integers
Source code for this entry:
Entry(ID("1d1653"),
    Formula(Equal(GCD(a, LCM(a, b)), Abs(a))),
    Variables(a, b),
    Assumptions(And(Element(a, ZZ), Element(b, ZZ))))

Topics using this entry

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