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Fungrim entry: 927e6e

lcm ⁣(a,b)=abgcd ⁣(a,b)\operatorname{lcm}\!\left(a, b\right) = \frac{\left|a b\right|}{\gcd\!\left(a, b\right)}
Assumptions:aZandbZand(a0orb0)a \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, b \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, \left(a \ne 0 \,\mathbin{\operatorname{or}}\, b \ne 0\right)
TeX:
\operatorname{lcm}\!\left(a, b\right) = \frac{\left|a b\right|}{\gcd\!\left(a, b\right)}

a \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, b \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, \left(a \ne 0 \,\mathbin{\operatorname{or}}\, b \ne 0\right)
Definitions:
Fungrim symbol Notation Short description
LCMlcm ⁣(a,b)\operatorname{lcm}\!\left(a, b\right) Least common multiple
Absz\left|z\right| Absolute value
GCDgcd ⁣(a,b)\gcd\!\left(a, b\right) Greatest common divisor
ZZZ\mathbb{Z} Integers
Source code for this entry:
Entry(ID("927e6e"),
    Formula(Equal(LCM(a, b), Div(Abs(Mul(a, b)), GCD(a, b)))),
    Variables(a, b),
    Assumptions(And(Element(a, ZZ), Element(b, ZZ), Or(Unequal(a, 0), Unequal(b, 0)))))

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2019-11-11 15:50:15.016492 UTC