Fungrim entry: 1d1653

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

Assumptions:

a \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
`GCD`	$\gcd\!\left(a, b\right)$	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("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

2021-03-15 19:12:00.328586 UTC