Step 1 :The problem is asking for the least common multiple (LCM) of the number of cups and napkins in a package. The LCM is the smallest number that is a multiple of both numbers.
Step 2 :We can find the LCM by using the formula \(\text{LCM}(a, b) = \frac{|a \times b|}{\text{gcd}(a, b)}\), where gcd is the greatest common divisor.
Step 3 :Given that there are 8 cups in a package and 12 napkins in a package, we find that the LCM is 24.
Step 4 :Therefore, Monique should buy \(\boxed{3}\) packages of cups and \(\boxed{2}\) packages of napkins to have an equal number of cups and napkins.