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Fungrim entry: 9500d3

lcm⁡ ⁣(na,nb)=∣n∣lcm⁡ ⁣(a,b)\operatorname{lcm}\!\left(n a, n b\right) = \left|n\right| \operatorname{lcm}\!\left(a, b\right)
Assumptions:a∈Z and⁡ b∈Z and⁡ n∈Za \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, b \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, n \in \mathbb{Z}
TeX:
\operatorname{lcm}\!\left(n a, n b\right) = \left|n\right| \operatorname{lcm}\!\left(a, b\right)

a \in \mathbb{Z} \,\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
Abs∣z∣\left|z\right| Absolute value
ZZZ\mathbb{Z} Integers
Source code for this entry:
Entry(ID("9500d3"),
    Formula(Equal(LCM(Mul(n, a), Mul(n, b)), Mul(Abs(n), LCM(a, b)))),
    Variables(a, b, n),
    Assumptions(And(Element(a, ZZ), Element(b, ZZ), Element(n, ZZ))))

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

2019-06-18 07:49:59.356594 UTC