So, for the first question, what you want is the smallest number, which prime factorisation contains both the factors of 168 and the factors of 324. (So, for every factor, you take whichever of the two numbers has a higher power for it and merge them)
this gives 2^3 (from 168) * 3^4 (from 324) * 7 (from 168) gives 4536. Do you understand my reasoning and why this always works?
For the second question, try and take the square root of a prime factorisation. What condition is true if and only if the number factorised is a perfect square?