# Fungrim entry: e74d86

$\operatorname{lcm}\!\left(a - b, b\right) = \frac{\left|a - b\right| \operatorname{lcm}\!\left(a, b\right)}{\left|a\right|}$
Assumptions:$a \in \mathbb{Z} \setminus \left\{0\right\} \;\mathbin{\operatorname{and}}\; b \in \mathbb{Z}$
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
LCM$\operatorname{lcm}\!\left(a, b\right)$ Least common multiple
Abs$\left|z\right|$ Absolute value
ZZ$\mathbb{Z}$ 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))))

## Topics using this entry

Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2021-03-15 19:12:00.328586 UTC