Least Number of Boxes to Buy Equal Chocolates from Packs of 24 and 15

Video Explanation

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

Solution

Question: Two brands of chocolates are available in packs of 24 and 15 respectively. If I need to buy an equal number of chocolates of both kinds, what is the least number of boxes of each kind I would need to buy?

Step 1: Identify the Mathematical Concept

To buy an equal number of chocolates from both brands using full packs only, we need to find the LCM (Least Common Multiple) of 24 and 15.

Step 2: Find the LCM of 24 and 15

24 = 2 × 2 × 2 × 3 = 2³ × 3

15 = 3 × 5

LCM = 2³ × 3 × 5 = 120

Step 3: Calculate the Number of Boxes

Number of boxes of first brand = 120 ÷ 24 = 5

Number of boxes of second brand = 120 ÷ 15 = 8

Final Answer

∴ The least number of boxes required are 5 boxes of the first brand and 8 boxes of the second brand.

Conclusion

Thus, by using the LCM of 24 and 15, we find that buying 5 and 8 boxes respectively gives the same number of chocolates with the least purchase.