10th Class Mathematics Real Numbers Question Bank Case Based (MCQs) - Real Numbers

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) 128

C) 288

D) 272

Correct Answer: C

Solution :

Sol. Using prime factorisation,

\[32=2\times 2\times 2\times 2\times 2={{2}^{5}}\]

and \[36=2\times 2\times 3\times 3={{2}^{2}}\times {{3}^{2}}\]

\[\therefore \] Minimum number of books \[LCM(32,36)\]

= Product of the greatest power of each prime factor in the numbers.

\[={{2}^{5}}\times {{3}^{2}}=32\times 9=288\]

So, option [c] is correct.