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

Hint: Here find the multiple of the numbers 32 and 36, but this multiple should be the least possible number. So, find the LCM of 32 and 36 to get the required answer.

Complete step-by-step answer:
In the question, we have to find the minimum number of books required for their class library of class X - section A and section B, so that they can be distributed equally among students of section A or section B. So here we need to get a smallest number that is a multiple of both the numbers 32 and 36. Or in other words we need a minimum number of books that are completely divisible by both the numbers 32 and 36. So here this is the concept of LCM. So, we will find the LCM or the least common multiple of each number, i.e. 32 and 36.
So, the LCM of 32 and 36 is found by the prime factorization method. The prime factorization of each numbers will be written as follows:
\[\Rightarrow 32=2\times 2\times \;2\times \;2\times 2\]
\[\Rightarrow 36=2\times 2\times 3\times 3\]
Now, the LCM of 32 and 36 will be:
\[\begin{align}
  & \Rightarrow LCM(32,36)\equiv 2\times 2\times \;2\times \;2\times 2\times 3\times 3 \\
 & \Rightarrow LCM(32,36)\equiv \text{288} \\
\end{align}\]
So the required number of books will be 288. Hence, the correct answer is option C) 288

Note: Here, we don’t have to find the H.C.F (Highest Common factor), because HCF will give a number that will be lesser than 32 and 36, so this can’t be possible, as the number of books required in the library has to be greater of equal to the numbers of students in each section.