Assume that the expressions given are denominators of fractions. Find the least common denominator.
-$m^{2}-5 m, m^{2}-11 m+30$
A) $(m+1)^{2}$
B) $m(m+1)(m-6)$
C) $m(m-5)(m-6)$
D) $\mathrm{m}(\mathrm{m}+1)^{2}$

Question

Quizplus · Accepted Answer

The least common denominator (LCD) is found by factoring each expression and then taking the product of the highest power of all factors present. The first expression, $m^2 - 5m$, factors into $m(m - 5)$. The second expression, $m^2 - 11m + 30$, factors into $(m - 5)(m - 6)$. The LCD must include all factors present in both expressions at the highest power they appear, which is $m(m - 5)(m - 6)$.

Assume That the Expressions Given Are Denominators of Fractions m2−5m,m2−11m+30m^{2}-5 m, m^{2}-11 m+30m2−5m,m2−11m+30

Assume That the Expressions Given Are Denominators of Fractions $m^{2}-5 m, m^{2}-11 m+30$