# Fungrim entry: 805c7a

$\operatorname{lcm}\!\left(a, b\right) = \min \left\{ m : m \in \mathbb{Z}_{\ge 1} \,\mathbin{\operatorname{and}}\, a \mid m \,\mathbin{\operatorname{and}}\, b \mid m \right\}$
Assumptions:$a \in \mathbb{Z} \setminus \left\{0\right\} \,\mathbin{\operatorname{and}}\, b \in \mathbb{Z} \setminus \left\{0\right\}$
TeX:
\operatorname{lcm}\!\left(a, b\right) = \min \left\{ m : m \in \mathbb{Z}_{\ge 1} \,\mathbin{\operatorname{and}}\, a \mid m \,\mathbin{\operatorname{and}}\, b \mid m \right\}

a \in \mathbb{Z} \setminus \left\{0\right\} \,\mathbin{\operatorname{and}}\, b \in \mathbb{Z} \setminus \left\{0\right\}
Definitions:
Fungrim symbol Notation Short description
LCM$\operatorname{lcm}\!\left(a, b\right)$ Least common multiple
Minimum$\mathop{\min}\limits_{P\left(x\right)} f\!\left(x\right)$ Minimum value of a set or function
SetBuilder$\left\{ f\!\left(x\right) : P\!\left(x\right) \right\}$ Set comprehension
ZZGreaterEqual$\mathbb{Z}_{\ge n}$ Integers greater than or equal to n
ZZ$\mathbb{Z}$ Integers
Source code for this entry:
Entry(ID("805c7a"),
Formula(Equal(LCM(a, b), Minimum(SetBuilder(m, m, And(Element(m, ZZGreaterEqual(1)), Divides(a, m), Divides(b, m)))))),
Variables(a, b),
Assumptions(And(Element(a, SetMinus(ZZ, Set(0))), Element(b, SetMinus(ZZ, Set(0))))))

## Topics using this entry

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

2019-08-21 11:44:15.926409 UTC