Fungrim entry: 5781de

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

Assumptions:

a \in \mathbb{Z} \setminus \left\{0\right\} \,\mathbin{\operatorname{and}}\, b \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, n \in \mathbb{Z}

TeX:

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

a \in \mathbb{Z} \setminus \left\{0\right\} \,\mathbin{\operatorname{and}}\, b \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, n \in \mathbb{Z}

Definitions:

Fungrim symbol	Notation	Short description
`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("5781de"),
    Formula(Equal(LCM(Add(a, b), b), Div(Mul(Abs(Add(a, b)), LCM(a, b)), Abs(a)))),
    Variables(a, b),
    Assumptions(And(Element(a, SetMinus(ZZ, Set(0))), Element(b, ZZ), Element(n, ZZ))))

Topics using this entry

Greatest common divisor