Question

In a school there are two sections, namely A and B, of class X. There are 30 students in section A and 28 students in section B. Find the minimum number of books required for their class library so that they can be distributed equally among students of section A or section B.

Answer 1

To distribute books equally among students of section A or B, we need to have a common factor that divides both 30 and 28. The common factor of 30 and 28 is 2.

So, we need to find the least common multiple (LCM) of 30 and 28, which is the smallest multiple that 30 and 28 have in common.

The prime factorization of 30 is 2 x 3 x 5, and the prime factorization of 28 is 2 x 2 x 7.

To find the LCM, we take the highest power of each prime factor that occurs in either number:

LCM = 2 x 2 x 3 x 5 x 7 = 420

Therefore, we need at least 420 books for the class library, so that they can be distributed equally among students of section A or B.