Fungrim entry: c4a892

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

Assumptions:

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

TeX:

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

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

Definitions:

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

Source code for this entry:

Entry(ID("c4a892"),
    Formula(Equal(LCM(a, GCD(b, c)), GCD(LCM(a, b), LCM(a, c)))),
    Variables(a, b, c),
    Assumptions(And(Element(a, ZZ), Element(b, ZZ), Element(c, ZZ))))

Topics using this entry

Greatest common divisor