Find the LCM.
-$r^{2}+6 r+9, r^{2}+3 r$
A) $r(r+1)(r+3)$
B) $r(r+3)$
C) $(r+3)^{2}$
D) $r(r+3)^{2}$

Question

Quizplus · Accepted Answer

The LCM of two algebraic expressions is the smallest expression that both original expressions can divide into. Factorizing the given expressions: $r^{2}+6r+9 = (r+3)^{2}$ and $r^{2}+3r = r(r+3)$. The LCM must include all factors present in the two expressions to the highest power they appear. Thus, $r(r+3)^{2}$ includes both the $r$ and $(r+3)^{2}$ factors, making it the correct LCM.

Find the LCM r2+6r+9,r2+3rr^{2}+6 r+9, r^{2}+3 rr2+6r+9,r2+3r A) r(r+1)(r+3)r(r+1)(r+3)r(r+1)(r+3) B) r(r+3)r(r+3)r(r+3) C) (r+3)2(r+3)^{2}(r+3)2 D) r(r+3)2r(r+3)^{2}r(r+3)2

Find the LCM $r^{2}+6 r+9, r^{2}+3 r$ A) $r(r+1)(r+3)$ B) $r(r+3)$ C) $(r+3)^{2}$ D) $r(r+3)^{2}$