Plastic plates come in packs of 8, plastic utensils come in packs of 12, and
plastic cups come in packs of 20. What are the least numbers of packs you
should buy in order to have the same number of plates, utensils, and cups?
60
To find the least number of packs you should buy in order 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 evenly divisible by all three numbers.
To find the LCM, we can use prime factorization. Let's break down each number into its prime factors:
8 = 2 x 2 x 2
12 = 2 x 2 x 3
20 = 2 x 2 x 5
To find the LCM, we need to take the highest power of each prime factor that appears in any of the numbers:
2^3 x 3 x 5 = 8 x 3 x 5 = 120
Therefore, the least number of packs you should buy to have the same number of plates, utensils, and cups is 120 packs.
LCM(8,12,20) = 120
Now you can figure how many packs of each make 120
233,450,707
;)