If $f\left(x\right)=\left(x^2-3x+2\right)\left(x^2-6x+p\right)$  and $g\left(x\right)=\left(x^2-4x+3\right)\left(x^2-8x+q\right)$ , then the value of $a$  and $b$  , if $\left(x-1\right)\left(x-2\right)$  is $\text{H}\text{.C}\text{.F}$  of $f\left(x\right)$  and $g\left(x\right)$  is

$=\left(x-1\right)\left(x-2\right)\left(x^2-6x+p\right)$

$g\left(x\right)=\left(x^2-4x+3\right)\left(x^2-8x+q\right)$

$g\left(x\right)=\left(x-1\right)\left(x-3\right)\left(x^2-8x+q\right)$

Given $\text{H}\text{.C}\text{.F}$  is $\left(x-1\right)\left(x-2\right)$

$\therefore$  The possible value of $\text{'}p\text{'}$  is any real value $p\in R$

If $\left(x^2-8x+q\right)$  is divisible by $\left(x-2\right)$

$\begin{array}{c}\text{then}4-16+q=0\\ q=12\end{array}$