The number of $12th$ roots of unity which are also the $18th$ root of unity is/are

$z^{\frac{1}{12}}=\cos \frac{2m\pi }{12}+i\sin \frac{2m\pi }{12}, \mathrm{m}=0,1,2,\dots \dots 11$

$z^{\frac{1}{18}}=\cos \frac{2n\pi }{18}+i\sin \frac{2n\pi }{18},n=0,1,2,\dots \dots 17$

Now, $\frac{2m\pi }{12}=\frac{2n\pi }{18}$

$\mathrm{m}=\frac{2\mathrm{n}}{3}; \therefore \mathrm{n}=0,3,6,9,12,15$

or $\mathrm{n}=\frac{3 \mathrm{m}}{2} \mathrm{m}=0,2,4,6,8,10$

$\therefore 6$ common roots