Find the LCD for the list of rational expressions.
-$\frac { 9 } { 16 x y } , \frac { 2 } { 20 x ^ { 2 } }$
A) $80 x y ^ { 3 }$
B) $80 x ^ { 2 } y$
C) $80 x ^ { 3 } y$
D) $80 x y ^ { 2 }$

Question

Find the LCD for the list of rational expressions.
-$\frac { 9 } { 16 x y } , \frac { 2 } { 20 x ^ { 2 } }$
A) $80 x y ^ { 3 }$
B) $80 x ^ { 2 } y$
C) $80 x ^ { 3 } y$
D)  $80 x y ^ { 2 }$

Quizplus · Accepted Answer

The least common denominator (LCD) for the given rational expressions $\frac { 9 } { 16 x y } , \frac { 2 } { 20 x ^ { 2 } }$ is found by identifying the least common multiple (LCM) of the denominators. The denominators are $16xy$ and $20x^2$. Factor each denominator to its prime factors: $16xy = 2^4xy$ and $20x^2 = 2^2 \cdot 5x^2$. The LCM must include each prime factor to its highest power present in any of the denominators, which gives $2^4 \cdot 5 \cdot x^2 \cdot y = 16 \cdot 5 \cdot x^2 \cdot y = 80x^2y$. Therefore, the LCD is $80x^2y$.

Find the LCD for the List of Rational Expressions 916xy,220x2\frac { 9 } { 16 x y } , \frac { 2 } { 20 x ^ { 2 } }16xy9​,20x22​

Find the LCD for the List of Rational Expressions $\frac { 9 } { 16 x y } , \frac { 2 } { 20 x ^ { 2 } }$