During a sale, color pencils were being sold in packs of 24 each and crayons in packs of 32 each. If you want full packs of both and the same number of pencils and crayons, how many of each would you need to buy?

The given problem is based on the concept of LCM.

Answer: We need to buy 4 packs of color pencils and 3 packs of crayons.

Let's understand the least common multiple and its applications in detail.

Explanation:

Numer of color pencils in each pack = 24 = 2 × 2 × 2 × 3

Number of crayons in each pack = 32 =  2 × 2 × 2 × 2 × 2

We need to buy full packs and the same number of color pencils and crayons, which implies the answer should be a multiple of both 24 and 32 and it should be least among such common multiples.

The LCM (24, 32)  = 2 × 2 × 2 × 2 × 2 × 3 = 96

So, in all, we need to buy 96 color pencils and 96 crayons.

Therefore,

• Number of color pencils packs = 96/24 = 4
• Number of crayons packs = 96/32 = 3

Thus, we need to buy 4 packs of color pencils and 3 packs of crayons in order to have the same number of color pencils and crayons.