a) 36\large\frac{1}{4}

b) 33\large\frac{3}{5}

c) 36\large\frac{4}{5}

d) 36\large\frac{3}{4}

correct answer is: d) 36\large\frac{3}{4}

Explanation

To find the required least number we need to find the LCM of given fraction 1\large\frac{3}{4}\normalsize,1\frac{5}{16}\normalsize,6\frac{1}{8} or \large\frac{7}{4},\frac{21}{16},\frac{49}{8}.
We know,
The formula we use to get the LCM of two or more fractions is:
\large\frac{The\ LCM\ of\ Numerator}{The\ HCF\ of\ Denominator}

\rightarrow LCM of Numerators 7,21,49 is =7\times3\times7=147
\rightarrow HCF of Denominators 4,6,8 is =4
So that, the LCM of 1\large\frac{3}{4}\normalsize,1\large\frac{5}{16}\normalsize,6\large\frac{1}{8} is =\large\frac{147}{4} or 36\large\frac{3}{4}
\therefore 36\large\frac{3}{4} is the least number which when divided by 1\large\frac{3}{4}\normalsize,1\large\frac{5}{16}\normalsize,6\large\frac{1}{8} , the quotients is a whole number.
Ans: 36\large\frac{3}{4} is the required least number.