The highest common factor of two numbers is 18.
The lowest common multiple of the two numbers is 324.
Both numbers are greater than 20. Find the two numbers. Answer ... and ...

1. Express the two numbers using their HCF

Let the two numbers be $18a$ and $18b$, where $a$ and $b$ are coprime.

Since the LCM is $324$,
$18ab=324$
$ab=18$

2. Find the coprime factor pair and calculate the numbers

The factor pairs of $18$ are
$(1,18),\ (2,9),\ (3,6).$

The pair must be coprime and both numbers must be greater than $20$.

$(2,9)$ is coprime, so the two numbers are
$18\times 2=36,$
$18\times 9=162.$