To find the least common denominator (LCD) of the fractions [tex]\(-\frac{2}{3n}\)[/tex] and [tex]\(\frac{7}{3}\)[/tex], we need to find the least common multiple (LCM) of their denominators.
The denominators of the fractions are:
[tex]\[ 3n \quad \text{and} \quad 3 \][/tex]
1. The first step is to identify the denominators.
- For [tex]\(-\frac{2}{3n}\)[/tex], the denominator is [tex]\(3n\)[/tex].
- For [tex]\(\frac{7}{3}\)[/tex], the denominator is [tex]\(3\)[/tex].
2. Next, find the LCM of these two denominators:
- The denominator [tex]\(3n\)[/tex] is already a product of [tex]\(3\)[/tex] and [tex]\(n\)[/tex].
- The denominator [tex]\(3\)[/tex] is just [tex]\(3\)[/tex].
3. To find the LCM, we need the smallest number that is a multiple of both [tex]\(3n\)[/tex] and [tex]\(3\)[/tex]. When considering multiples, remember that [tex]\(3n\)[/tex] already includes the [tex]\(3\)[/tex] factor multiplied by [tex]\(n\)[/tex].
Therefore, the least common multiple of [tex]\(3n\)[/tex] and [tex]\(3\)[/tex] is:
[tex]\[ 3n \][/tex]
So, the least common denominator (LCD) of [tex]\(-\frac{2}{3n}\)[/tex] and [tex]\(\frac{7}{3}\)[/tex] is:
[tex]\[ \boxed{3n} \][/tex]
