Question

In a school there are two sections of class X - section A and section B There are 32 students in section A and 36 students in section B Determine 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

• A. 258
• B. 268
• C. 288
• D. 298

Answer 1

Answer: (C)

288

It is given that there are $32$ students in section A and $36$ students in section B.

To determine the minimum number of books required to distribute equally among students of section A and section B, we need to find the LCM of $32$ and $36$.

To find the LCM, we find the prime factors of $32$ and $36$ as follows:

Prime factors of $32$ are $2$. Prime factorization of $32$ in exponential form is:

$32=2^5$

Prime factors of $36$ are $2,3$. Prime factorization of $36$ in exponential form is:

$36=2^2\times 3^2$

Now multiplying the highest exponent prime factors to calculate the LCM of $32$ and $36$, we have:

LCM$(32,36)=2^5\times 3^2=288$

Hence, the minimum number of books required to distribute equally among students of section A and section B are $288$.