Question

Find the L.C.M. of the two expressions $a^2+7a-18$ and $a^2+10a+9$ with the help of their H.C.F.

• A. $(a-2)(a+9)(a+1)$
• B. $(a-2{)}^2(a+9\left)\right(a+1)$
• C. $(a-2)(a+9{)}^2(a+1)$
• D. $(a-2)(a+9)(a-9)$

Answer 1

The correct option is A $(a-2)(a+9)(a+1)$

First expression $=a^2+7a-18$
$=a^2+9a-2a-18$
$=a(a+9)-2(a+9)$
$=(a+9)(a-2)$

Second expression $=a^2+10a+9$
$=a^2+9a+a+9$
$=a(a+9)+(a+9)$
$=(a+9)(a+1)$

$\therefore$ H.C.F = $(a+9)$

L.C.M = Product of the two expressions/H.C.F

$\Rightarrow$ L.C.M $=\frac{(a^2+7a-18)(a^2+10a+9)}{a+9}$
$=\frac{(a+9)(a-2)(a+9)(a+1)}{a+9}$
$=(a-2)(a+9)(a+1)$