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Fungrim entry: 5781de

lcm ⁣(a+b,b)=a+blcm ⁣(a,b)a\operatorname{lcm}\!\left(a + b, b\right) = \frac{\left|a + b\right| \operatorname{lcm}\!\left(a, b\right)}{\left|a\right|}
Assumptions:aZ{0}andbZandnZa \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
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("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))))

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2019-10-05 13:11:19.856591 UTC