Same Number of Colour Pencils and Crayons in Full Packs (24 and 32)

Video Explanation

Watch the video below to understand the complete solution step by step:

Solution

Question: During a sale, colour 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?

Step 1: Identify the Mathematical Concept

To get the same number of colour pencils and crayons using full packs only, we need to find the LCM (Least Common Multiple) of 24 and 32.

Step 2: Find the LCM of 24 and 32

24 = 2 × 2 × 2 × 3 = 2³ × 3

32 = 2 × 2 × 2 × 2 × 2 = 2⁵

LCM = 2⁵ × 3 = 96

Step 3: Interpret the Result

This means we must buy:

96 colour pencils

96 crayons

Number of pencil packs = 96 ÷ 24 = 4

Number of crayon packs = 96 ÷ 32 = 3

Final Answer

∴ You need to buy 96 colour pencils and 96 crayons.

Conclusion

Thus, by using the LCM of 24 and 32, we find that buying 96 of each ensures full packs and the same number of colour pencils and crayons.