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Fungrim entry: 7009cc

lcm ⁣(a,gcd ⁣(a,b))=a\operatorname{lcm}\!\left(a, \gcd\!\left(a, b\right)\right) = \left|a\right|
Assumptions:aZandbZa \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, b \in \mathbb{Z}
TeX:
\operatorname{lcm}\!\left(a, \gcd\!\left(a, b\right)\right) = \left|a\right|

a \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, b \in \mathbb{Z}
Definitions:
Fungrim symbol Notation Short description
LCMlcm ⁣(a,b)\operatorname{lcm}\!\left(a, b\right) Least common multiple
GCDgcd ⁣(a,b)\gcd\!\left(a, b\right) Greatest common divisor
Absz\left|z\right| Absolute value
ZZZ\mathbb{Z} Integers
Source code for this entry:
Entry(ID("7009cc"),
    Formula(Equal(LCM(a, GCD(a, b)), Abs(a))),
    Variables(a, b),
    Assumptions(And(Element(a, ZZ), Element(b, ZZ))))

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2020-01-31 18:09:28.494564 UTC