Symbols:Abbreviations/L

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L

LCM, lcm or l.c.m.

The lowest (or least) common multiple.

LHS

Left hand side.

In an equation:

$\text {Expression $1$} = \text {Expression $2$}$

the term $\text {Expression $1$}$ is the left hand side.

LQR

Law of Quadratic Reciprocity.

Let $p$ and $q$ be distinct odd primes.

Then:

$\paren {\dfrac p q} \paren {\dfrac q p} = \paren {-1}^{\dfrac {\paren {p - 1} \paren {q - 1} } 4}$

where $\paren {\dfrac p q}$ and $\paren {\dfrac q p}$ are defined as the Legendre symbol.

An alternative formulation is: $\paren {\dfrac p q} = \begin{cases} \quad \paren {\dfrac q p} & : p \equiv 1 \lor q \equiv 1 \pmod 4 \\ -\paren {\dfrac q p} & : p \equiv q \equiv 3 \pmod 4 \end{cases}$

The fact that these formulations are equivalent is immediate.

This fact is known as the Law of Quadratic Reciprocity, or LQR for short.

lsb or l.s.b.

Least significant bit.

LSC

Lower semicontinuous.

lub or l.u.b.

Least upper bound.

Another term for supremum.

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