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Fungrim entry: cb9f61

lcm ⁣(ad,bd)=lcm ⁣(a,b)d\operatorname{lcm}\!\left(\frac{a}{d}, \frac{b}{d}\right) = \frac{\operatorname{lcm}\!\left(a, b\right)}{\left|d\right|}
Assumptions:aZ  and  bZ  and  dZ  and  da  and  dba \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; b \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; d \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; d \mid a \;\mathbin{\operatorname{and}}\; d \mid b
\operatorname{lcm}\!\left(\frac{a}{d}, \frac{b}{d}\right) = \frac{\operatorname{lcm}\!\left(a, b\right)}{\left|d\right|}

a \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; b \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; d \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; d \mid a \;\mathbin{\operatorname{and}}\; d \mid b
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(Div(a, d), Div(b, d)), Div(LCM(a, b), Abs(d)))),
    Variables(a, b, d),
    Assumptions(And(Element(a, ZZ), Element(b, ZZ), Element(d, ZZ), Divides(d, a), Divides(d, b))))

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2021-03-15 19:12:00.328586 UTC