Arrange the following in ascending order-

$\frac{13}{27},\frac{17}{35},\frac{13}{36},\frac{12}{25}$

The given fraction $\frac{13}{27},\frac{17}{35},\frac{13}{36},\frac{12}{25}$

LCM of $25,27,35,36is18900$

Now, we will write each fraction in such a way that they have the same denominator$=18900$

$$\begin{gathered} \frac{13}{27}=\frac{13\times 700}{27\times 700}=\frac{9100}{18900} \\ \frac{17}{35}=\frac{17\times 540}{35\times 540}=\frac{9180}{18900} \\ \frac{13}{36}=\frac{13\times 525}{36\times 525}=\frac{6825}{18900} \\ \frac{12}{25}=\frac{12\times 756}{25\times 756}=\frac{9072}{18900} \end{gathered}$$

Clearly, $6825<9072<9100<9180$

$$\begin{gathered} \Rightarrow \frac{6825}{18900}<\frac{9072}{18900}<\frac{9100}{18900}<\frac{9180}{18900} \\ \Rightarrow \frac{13}{36}<\frac{12}{25}<\frac{13}{27}<\frac{17}{35} \end{gathered}$$

Hence, the ascending order is $\frac{13}{36}<\frac{12}{25}<\frac{13}{27}<\frac{17}{35}$.