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Fungrim entry: c4a892

lcm ⁣(a,gcd ⁣(b,c))=gcd ⁣(lcm ⁣(a,b),lcm ⁣(a,c))\operatorname{lcm}\!\left(a, \gcd\!\left(b, c\right)\right) = \gcd\!\left(\operatorname{lcm}\!\left(a, b\right), \operatorname{lcm}\!\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}
\operatorname{lcm}\!\left(a, \gcd\!\left(b, c\right)\right) = \gcd\!\left(\operatorname{lcm}\!\left(a, b\right), \operatorname{lcm}\!\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
LCMlcm ⁣(a,b)\operatorname{lcm}\!\left(a, b\right) Least common multiple
GCDgcd ⁣(a,b)\gcd\!\left(a, b\right) Greatest common divisor
ZZZ\mathbb{Z} Integers
Source code for this entry:
    Formula(Equal(LCM(a, GCD(b, c)), GCD(LCM(a, b), LCM(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