Question

The H.C.F of $a^2-5a+6$ and $a-3$ is $a-2$. Find their L.C.M.

• A. $(a-3)$
• B. $(a-3{)}^2$
• C. $(a-2{)}^2$
• D. $(a-2)(a-3{)}^2$

Answer 1

The correct option is B $(a-3{)}^2$

Given:
$f\left(x\right)=a^2-5a+6$
$g\left(x\right)=a-3$
H.C.F $=$ $a-2$
Factor of $a^2-5a+6=(a-2)(a-3)$
Using the formula,
$f\left(x\right)\times g\left(x\right)=H.C.F\times L.C.M$
L.C.M $=$ $\frac{(a-2)(a-3)(a-3)}{(a-2)}$
L.C.M $=$ $(a-3{)}^2$