Find the least common denominator of the rational expressions.
-$\frac { 1 } { 40 x } , \frac { 1 } { 5 x ^ { 2 } }$, and $\frac { 1 } { 8 x ^ { 3 } }$
A) $40 x ^ { 2 }$
B) $40 x ^ { 5 }$
C) $8 x ^ { 3 }$
D) $40 x ^ { 3 }$

Question

Quizplus · Accepted Answer

The least common denominator (LCD) of the given fractions must account for the highest powers of all prime factors present in the denominators. The prime factorization of 40 is $2^3 \cdot 5$, and the highest power of $x$ present is $x^3$. Therefore, the LCD is $2^3 \cdot 5 \cdot x^3 = 40x^3$.

Find the Least Common Denominator of the Rational Expressions 140x,15x2\frac { 1 } { 40 x } , \frac { 1 } { 5 x ^ { 2 } }40x1​,5x21​

Find the Least Common Denominator of the Rational Expressions $\frac { 1 } { 40 x } , \frac { 1 } { 5 x ^ { 2 } }$