The period of
is
.
Recall that
and
both have periods of
. This means


Replacing
with
, we have

In other words, if we change
by some multiple of
, we end up with the same output. So
has period
.
Similarly,
has a period of
,

We want to find the period
of
, such that


On the left side, we have

and

So, in terms of its period, we have

and we need to find the smallest positive
such that

which points to
, since

