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?

Options

• 144

• 2

• 420

• 272

Answer 1

420

Explanation:

Prime factorization of the numbers:

28 = 2² × 7

28 = 2 × 2 × 7

30 = 2 × 3 × 5

To calculate the LCM, we take the highest power of every prime factor present in the factorizations:

LCM = 2² × 3 × 5 × 7

LCM = 4 × 3 × 5 × 7

LCM = 12 × 35

LCM = 420

Thus, 420 is the smallest number divisible by both student counts.