$\begin{array}{l}\text{Let the number be x.}\\ \\ \text{Then,\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}\frac{1}{4}\times \frac{3}{5}\times \frac{6}{5}\times x=54\\ \\ \Rightarrow \frac{18}{100}\times x=54\\ \\ \Rightarrow x=\frac{54\times 100}{18}=300\\ \\ \therefore \text{\hspace{0.17em}\hspace{0.17em}The number is 300.}\end{array}$

Hence, option D is correct.