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

To solve this problem, we need to find the minimum number of books that can be distributed equally among students of either Section A or Section B. This requires determining the Least Common Multiple (LCM) of the number of students in Section A and Section B.

1. Identify the number of students in each section:
   • Section A: 28 students
   • Section B: 30 students
2. Calculate the LCM of the numbers 28 and 30. The LCM is the smallest positive integer that is divisible by both these numbers.
3. Find the prime factorization of each number:
   • 28: \(28 = 2^2 \times 7\)
   • 30: \(30 = 2 \times 3 \times 5\)
4. Determine the LCM by taking the highest power of each prime number present in the factorizations:
   • For 2: highest power is \(2^2\)
   • For 3: highest power is \(3^1\)
   • For 5: highest power is \(5^1\)
   • For 7: highest power is \(7^1\)
5. Compute the LCM: \(\text{LCM} = 2^2 \times 3^1 \times 5^1 \times 7^1 = 4 \times 3 \times 5 \times 7 = 420\)
6. Therefore, the smallest number of books needed to distribute them equally among students of either section is 420.

Hence, the correct answer is 420.