Convert the denominator to same by taking LCM.
LCM OF 7,3,4, 5 is 420.
Therefore,
[tex]\begin{gathered} \frac{4}{7}=\frac{240}{420} \\ \frac{2}{3}=\frac{280}{420} \\ \frac{1}{4}=\frac{105}{420} \\ \frac{3}{5}=\frac{252}{420} \end{gathered}[/tex]Here, denominators are same. Therefore, the least of it will be the least of the numerator.
[tex]\begin{gathered} \frac{105}{420}<\frac{240}{420}<\frac{252}{420}<\frac{280}{420} \\ \frac{1}{4}<\frac{4}{7}<\frac{3}{5}<\frac{2}{3} \end{gathered}[/tex]