Question

Find the least common denominator. $$\frac{1}{x}, \frac{x}{3}, \frac{2}{3 x}$$

Short answer

Therefore, the least common denominator of the given fractions is \(3x\).

Step-by-step solution

Write the denominators

The denominators of the fractions are \(x\), \(3\), and \(3x\).

Find the LCM of the denominators

We need to find the least common multiple (LCM) of \(x\), \(3\), and \(3x\). The LCM of a set of numbers is the smallest positive integer that is a multiple of each of the numbers in the set. In this case, \(3x\) is already a multiple of both \(x\) and \(3\), hence the LCM is \(3x\).

LCD is the LCM

Therefore, the least common denominator (LCD) of the given fractions is the LCM of their denominators. Hence, the LCD is \(3x\).