Clarify mathematical definition of `lcm` (#56992)
Some folks define `lcm(x::T,y::T)` as any `z::T` such that there exists
`a::T, b::T` with `a*x==z` and `b*y==z` and for all `zʹ::T` such that
there exist `a::T, b::T` with `a*x==zʹ` and `b*y==zʹ`, there also exists
`c::T` with `z*c==zʹ`. This is a reasonable definition, but not what we
use. Notably, it makes `lcm(x::Rational, y::Rational) = z::Rational`
true for all finite, nonzero `x`, `y`, and `z`.
The definition we use requires `a`, `b`, and `c` to all be _integers_,
not rationals in the case of `lcm(x::Rational, y::Rational)`. This
clarifies what we mean when we define `lcm(x::Rational, y::Rational)`
and also how the generic function should be extended.
See [this
thread](https://github.com/JuliaLang/julia/pull/56423#discussion_r1826999933)
for more discussion
