Question

There are two sections A and B of Grade X. There are 28 students in Section A and 30 students in Section B. What is the minimum number of books you will acquire for the class library so that they can be distributed equally among students of Section A or Section B ?

• A. 144
• B. 2
• C. 420
• D. 272

Hint:

Whenever a question asks for a "minimum" quantity that satisfies multiple distribution conditions, it is a direct application of LCM. If it asks for "maximum" size of a group/container, use HCF.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
To distribute books equally among either 28 or 30 students, the total number of books must be a multiple of both 28 and 30. The "minimum" number implies finding the Least Common Multiple (LCM).
Step 2: Key Formula or Approach:
Find the LCM of 28 and 30 using the prime factorization method.
Step 3: Detailed Explanation:
Prime factorization of the numbers:
\[ 28 = 2 \times 2 \times 7 = 2^2 \times 7 \]
\[ 30 = 2 \times 3 \times 5 \]
To calculate the LCM, we take the highest power of every prime factor present in the factorizations:
\[ \text{LCM} = 2^2 \times 3 \times 5 \times 7 \]
\[ \text{LCM} = 4 \times 3 \times 5 \times 7 \]
\[ \text{LCM} = 12 \times 35 \]
\[ \text{LCM} = 420 \]
Thus, 420 is the smallest number divisible by both student counts.
Step 4: Final Answer:
The minimum number of books required is 420.