Problem

PART B Monique wants to have an equal number of cups and napkins. Whe is the least number of packages of cups and the least number of packages of napkins Monique should buy to have an equal number of cups and napkins? Justify your answer. 6.NSO.3.1

Solution

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.

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