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Fungrim entry: 1bbdaf

lcm ⁣(a+nb,b)=a+nblcm ⁣(a,b)a\operatorname{lcm}\!\left(a + n b, b\right) = \frac{\left|a + n b\right| \operatorname{lcm}\!\left(a, b\right)}{\left|a\right|}
Assumptions:aZ{0}  and  bZ  and  nZa \in \mathbb{Z} \setminus \left\{0\right\} \;\mathbin{\operatorname{and}}\; b \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; n \in \mathbb{Z}
\operatorname{lcm}\!\left(a + n b, b\right) = \frac{\left|a + n b\right| \operatorname{lcm}\!\left(a, b\right)}{\left|a\right|}

a \in \mathbb{Z} \setminus \left\{0\right\} \;\mathbin{\operatorname{and}}\; b \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; n \in \mathbb{Z}
Fungrim symbol Notation Short description
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(LCM(Add(a, Mul(n, b)), b), Div(Mul(Abs(Add(a, Mul(n, b))), LCM(a, b)), Abs(a)))),
    Variables(a, b, n),
    Assumptions(And(Element(a, SetMinus(ZZ, Set(0))), Element(b, ZZ), Element(n, ZZ))))

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2021-03-15 19:12:00.328586 UTC