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Fungrim entry: 8dc1c9

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

a \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; b \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; c \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
ZZZ\mathbb{Z} Integers
Source code for this entry:
    Formula(Equal(GCD(a, LCM(b, c)), LCM(GCD(a, b), GCD(a, c)))),
    Variables(a, b, c),
    Assumptions(And(Element(a, ZZ), Element(b, ZZ), Element(c, ZZ))))

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2021-03-15 19:12:00.328586 UTC