Miss Anaya is buying pencils in packs of 12, notebooks in paakcs of 16, and red pens in packs of 20. She needs to buy the same number of pencils, notebooks, and red pens. What is the least number of packs of each item that she can buy?
of course the bot gives no explanation of its answer ....
(which also happens to be wrong)
We are looking or the GCM of 12, 16, and 20
12 = 3*4
16 = 4*4
20 = 5*4
So the GCM would be 3*4*4*5 = 240
so ...
240/12 or 20 packs of pencils, number of pencils bought = 240
240/16 or 15 packs of notebooks , number of notebooks bought = 240
240/20 or 12 packs of red pens , number of red pens bought = 240
The bot's answer of 4 packs of each would give us
48 pencils
60 notebooks
and 80 red pens, but they should be the same!!!
To find the least number of packs of each item that Miss Anaya can 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 from the factorizations:
2^4 * 3 * 5
Step 3: Multiply the factors together:
2 * 2 * 2 * 2 * 3 * 5 = 240
Therefore, Miss Anaya must buy 240 pencils, 240 notebooks, and 240 red pens, which corresponds to packs of 20 pencils (240/12), 15 notebooks (240/16), and 12 red pens (240/20).
To find the least number of packs of each item that Miss Anaya can buy, we need to find the least common multiple (LCM) of 12, 16, and 20.
First, let's list the multiples of each number until we find a common multiple:
Multiples of 12: 12, 24, 36, 48, 60, 72, 84, 96, 108, ...
Multiples of 16: 16, 32, 48, 64, 80, 96, 112, ...
Multiples of 20: 20, 40, 60, 80, 100, 120, ...
From the lists of multiples, we can see that the least common multiple (LCM) of 12, 16, and 20 is 48.
Therefore, Miss Anaya needs to buy 48 pencils in packs of 12 (48/12 = 4 packs), 48 notebooks in packs of 16 (48/16 = 3 packs), and 48 red pens in packs of 20 (48/20 = 2 packs) in order to have an equal number of each item.