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Fungrim entry: e74d86

lcm⁡ ⁣(a−b,b)=∣a−b∣lcm⁡ ⁣(a,b)∣a∣\operatorname{lcm}\!\left(a - b, b\right) = \frac{\left|a - b\right| \operatorname{lcm}\!\left(a, b\right)}{\left|a\right|}
Assumptions:a∈Z∖{0}  and⁡  b∈Za \in \mathbb{Z} \setminus \left\{0\right\} \;\mathbin{\operatorname{and}}\; b \in \mathbb{Z}
TeX:
\operatorname{lcm}\!\left(a - b, b\right) = \frac{\left|a - 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}
Definitions:
Fungrim symbol Notation Short description
LCMlcm⁡ ⁣(a,b)\operatorname{lcm}\!\left(a, b\right) Least common multiple
Abs∣z∣\left|z\right| Absolute value
ZZZ\mathbb{Z} Integers
Source code for this entry:
Entry(ID("e74d86"),
    Formula(Equal(LCM(Sub(a, b), b), Div(Mul(Abs(Sub(a, b)), LCM(a, b)), Abs(a)))),
    Variables(a, b),
    Assumptions(And(Element(a, SetMinus(ZZ, Set(0))), Element(b, ZZ))))

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2021-03-15 19:12:00.328586 UTC