Question

What is the least number which when divided by $36,38,57,114$ and $19$ leaves the remainder $26,28,47,104$ and $9$, respectively?

• A. $19826$
  
• B. $19836$
• C. $19846$
  
• D. None of these

Answer 1

The correct option is A $19826$

$\because$ Divided $=$ Division$\times$Quotient$+$Remainder$.$

Let $x=36\times m+26x=38\times n+28x=57\times o+47x=114\times p+104x=19\times q+9$

$\because$ Difference of division and remainder is correct i.e,$10.$

Now LCM of $30,38,57,114,19.$

This step refers to the image$.$

$36=4\times 9=2^2\times 958=2\times 2957=19\times 3114=2\times 19\times 319=19$

LCM of $(36,58,57,114,19)=2\times 29\times 19\times 3=19836$

Hence the least no$:$ $=19836-10=19826.$