PS : please draw it on paper for better visualizing.
given that, 18 x 30
if i cut, $\color{red}{\underline{\text{18 x 18 }}}$ in 18 x 30 ====> remaining piece 18 x 12
if i cut, $\color{green}{\underline{\text{12 x 12 }}}$ in 18 x 12 ====> 6 x 12
if i cut, $\color{blue}{\underline{\text{6 x 6 }}}$ in 6 x 12 ====> $\color{magenta}{\underline{\text{6 x 6 }}}$.
remaining piece is also square, So stop here !
For getting least number of equal pieces, we have to cut each piece as much as big. But our final square is 6 x 6
So, We have to cut each piece as 6 x 6.
i) $\color{red}{\underline{\text{18 x 18 }}}$ we can cut this piece into 9 pieces of 6 x 6.
ii) $\color{green}{\underline{\text{12 x 12 }}}$ we can cut this piece into 4 pieces of 6 x 6.
iii) $\color{blue}{\underline{\text{6 x 6 }}}$ --- only 1 piece of 6 x 6
iv) $\color{magenta}{\underline{\text{6 x 6 }}}$ --- only 1 piece of 6 x 6
Total = 9+4+1+1 = 15
