Find the least common denominator.
-$\frac { 8 } { 20 x y } + \frac { 7 } { 16 x ^ { 2 } }$
A) $80 x ^ { 2 } y$
B) $80 x y ^ { 2 }$
C) $80 x ^ { 3 } y$
D) $80 x y ^ { 3 }$

Question

Quizplus · Accepted Answer

The least common denominator (LCD) must account for all factors present in the denominators of the fractions, with the highest power of each. The denominators are $20xy$ and $16x^2$. Factorizing, we get $20 = 2^2 \cdot 5$ and $16 = 2^4$, so the LCD must include $2^4$ (the higher power of 2 between $2^2$ and $2^4$), $x^2$ (the higher power of $x$ between $x$ and $x^2$), and $y$ (since it's only in one denominator). Thus, the LCD is $2^4 \cdot 5 \cdot x^2 \cdot y = 16 \cdot 5 \cdot x^2 \cdot y = 80x^2y$.

Find the Least Common Denominator 820xy+716x2\frac { 8 } { 20 x y } + \frac { 7 } { 16 x ^ { 2 } }20xy8​+16x27​

Find the Least Common Denominator $\frac { 8 } { 20 x y } + \frac { 7 } { 16 x ^ { 2 } }$