Chapter 6.6, Problem 7MRE

To determine

To find: The least common denominator.

Answer to Problem 7MRE

The least common denominator of $\frac{1}{2xy},\frac{3}{x^2}$ is $2x^{2}y$.

Explanation of Solution

Given information:

The fractions $\frac{1}{2xy},\frac{3}{x^2}$.

Formula used:

To find least common denominator:

Firstly, the LCM of all the constant is find out.

Then, the highest value of each variable is taken.

Then, all the highest value of variables and LCM of constant is multiplied to make it the least common denominator.

  $\frac{1}{2xy},\frac{3}{x^2}$

The constant in both fractions are 2 and 1. So, LCM of 2 and 1 is 2.

Variables:

  $x$ : The term of variable $x$ in denominator are $x$ and $x^2$ . So highest term is $x^2$.

  $y$ : The term of variable $y$ in denominator is $y$ . So highest term is $y$.

So,

Least common denominator:

  $\begin{array}{l}=2\cdot x^2\cdot y\\ =2x^{2}y\end{array}$

The least common denominator of $\frac{1}{2xy},\frac{3}{x^2}$ is $2x^{2}y$.