question_answer

The least number which when divided by 24, 32 and 36 leaves the remainders 19, 27 and 31 respectively, is

A) 283                  

B) 288

C) 293                              

D) 299

Correct Answer: A

Solution :

    

Here,     \[24-19=5\]

\[32-27=5\]

and                   \[36-31=5\]

LCM of (24, 32, 36)

\[\therefore \] \[LCM=2\times 2\times 2\times 3\times 4\times 3=288\]

\[\therefore \] Required number \[=288-5=283\]