Question

Plastic plates come in packs of 8, plastic utensils come i packs of 12, and plastic cups come in packs of 20. What are the least number of packs you should buy in offer to have the same number of plates , utensils, and cups.

Answer 1

To have the same number of plates, utensils, and cups, you need to find the least common multiple (LCM) of 8, 12, and 20. The LCM is 120, so you would need to buy at least 120 plates, utensils, and cups.

Step-by-step explanation:

To have the same number of plates, utensils, and cups, we need to find the least common multiple (LCM) of 8, 12, and 20. The LCM is the smallest number that is divisible by all three numbers.

Prime factorize each number: 8 = 2^3, 12 = 2^2 * 3, 20 = 2^2 * 5.

To find the LCM, we take the highest power of each prime factor: 2^3 * 3 * 5 = 120.

Therefore, you would need to buy at least 120 plates (15 packs of 8), 120 utensils (10 packs of 12), and 120 cups (6 packs of 20) to have the same number of each item.