The total number of 3 -digit numbers, whose greatest common divisor...

Prime factorisation of $36 = 2 \times 2 \times 3 \times 3$

So, for number having G.C.D with $36$ to be $2$, the number should be odd multiple of $2$ and does not have factor $3$ and $9$

$⇒$Odd multiple of $2$ are

\left\{102, 106, 110, 114 \ldots \ldots . 998\right\}\left(225\text{numbers}\right)$</p><p>$⇒$No. of multiples of$3$are</p><p>\left\{102, 114, 126 \ldots \ldots . 990\right\}\left(75\text{numbers}\right)$

Which also include multiple of $9$

Hence, Required $= 225 - 75 = 150$