Cups are sold 6 to a package and plates are sold 8 to a package. If you want to have the same number of each item for a party, what is the least number of packages of each you need to buy?
The answer is 24
To determine the least number of packages of cups and plates you need to buy, we need to find the least common multiple (LCM) of 6 and 8. The LCM is the smallest number that is divisible by both 6 and 8.
To find the LCM of 6 and 8, we can use the prime factorization method:
Step 1: Find the prime factors of each number.
- Prime factors of 6: 2 x 3
- Prime factors of 8: 2 x 2 x 2
Step 2: Take the highest power of each prime factor that appears in either number.
- The highest power of 2 is 2^3 = 8.
- The highest power of 3 is 3^1 = 3.
Step 3: Multiply the highest powers of each prime factor together.
- LCM = 8 x 3 = 24.
Therefore, the least number of packages of cups and plates you need to buy is 24. You will need to buy 24 cups in 4 packages (24 ÷ 6 = 4) and 24 plates in 3 packages (24 ÷ 8 = 3).