Find the LCM.
-$r^{2}+10 r+25, r^{2}+5 r$
A) $r(r+1)(r+5)$
B) $r(r+5)$
C) $(r+5)^{2}$
D) $r(r+5)^{2}$

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: $r^{2}+10r+25 = (r+5)^{2}$ and $r^{2}+5r = r(r+5)$. The LCM must include all factors present in the two expressions at their highest powers, which is $r$ and $(r+5)^{2}$, making the LCM $r(r+5)^{2}$.

Find the LCM r2+10r+25,r2+5rr^{2}+10 r+25, r^{2}+5 rr2+10r+25,r2+5r A) r(r+1)(r+5)r(r+1)(r+5)r(r+1)(r+5) B) r(r+5)r(r+5)r(r+5) C) (r+5)2(r+5)^{2}(r+5)2 D) r(r+5)2r(r+5)^{2}r(r+5)2

Find the LCM $r^{2}+10 r+25, r^{2}+5 r$ A) $r(r+1)(r+5)$ B) $r(r+5)$ C) $(r+5)^{2}$ D) $r(r+5)^{2}$