Question

sheila is buying paper plates and cups for her sons third birthday party. paper plates come in sets of 24 and cups come in sets of 5. if sheila wants the same number of each item, what is the minimum number of items she must purchase?

Explanation:

Step1: Find LCM of 24 and 5

To find the least common multiple (LCM) of 24 and 5, we note that 24 and 5 are coprime (their GCD is 1). So, \( LCM(24, 5)=24\times5 = 120 \). This is the number of each item (plates and cups) she needs.

Step2: Calculate total items

Since she needs 120 plates and 120 cups, the total number of items is \( 120 + 120=240 \).

Answer:

240