Fungrim home page

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}  and  bZa \in \mathbb{Z} \setminus \left\{0\right\} \;\mathbin{\operatorname{and}}\; b \in \mathbb{Z}
\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}
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:
    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))))

Topics using this entry

Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2021-03-15 19:12:00.328586 UTC