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Fungrim entry: 1d1653

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

a \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; b \in \mathbb{Z}
Fungrim symbol Notation Short description
GCDgcd ⁣(a,b)\gcd\!\left(a, b\right) Greatest common divisor
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(GCD(a, LCM(a, b)), Abs(a))),
    Variables(a, b),
    Assumptions(And(Element(a, ZZ), Element(b, ZZ))))

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2021-03-15 19:12:00.328586 UTC