Miss Jennifer is buying pencils in packs of 12, notebooks in packs of 16, and red pens in boxes of 20. She needs to have the same number of pencils, notebooks, and red pens. What is the smallest number of packs of each type that she should buy?
Answer:
Miss Jennifer needs to buy
packs of pencils,
packs of notebooks and
packs of red pens.
To find the smallest number of packs of each type that Miss Jennifer should buy, we need to find the least common multiple (LCM) of 12, 16, and 20.
Step 1: Find the prime factorization of each number:
12 = 2^2 * 3
16 = 2^4
20 = 2^2 * 5
Step 2: Take the highest power of each prime factor that appears in any of the numbers:
2^4 * 3 * 5 = 240
So, Miss Jennifer should buy 240 packs of pencils, 240 packs of notebooks, and 240 packs of red pens in order to have the same number of each.
This is similar to finding the lowest common multiple
12 = 4*3
16 = 4*4
20 = 4*5
LCM = 4*4*3*5 = 240
packs of pencils = 240/12 = 20
packs of notebooks = ...
packs of red pens = ...