Fungrim entry: 6572c5

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

Assumptions:

a \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, b \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, a \ne 0 \,\mathbin{\operatorname{and}}\, b \ne 0

TeX:

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

a \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, b \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, a \ne 0 \,\mathbin{\operatorname{and}}\, b \ne 0

Definitions:

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

Source code for this entry:

Entry(ID("6572c5"),
    Formula(Equal(GCD(a, b), Div(Abs(Mul(a, b)), LCM(a, b)))),
    Variables(a, b),
    Assumptions(And(Element(a, ZZ), Element(b, ZZ), Unequal(a, 0), Unequal(b, 0))))

Topics using this entry

Greatest common divisor