It's pretty easy to see that both numbers are divisible by 5, so
let's start there. You can fit 5 into 30 a grand total of 6 times, and
45 divided by 5 is 9. So our new fraction is . But hold the phone!
(We were speaking figuratively - you can put the phone down now) Each of
those numbers is divisible by 3. Do our thing one more time and
we're left with , which can no longer be reduced. Not without a
hacksaw, anyway.

Example 2

Reduce to its lowest terms.

We've got a couple of even numbers here, so clearly 2 will divide
both the numerator and denominator. We start by reducing this fraction
to , but we've still got two even numbers, so we do it again. Now
we've got . There are no natural numbers (except 1) that divide 30
and 23, so the fraction is in lowest terms.