College

What is the least common denominator of [tex]\frac{2}{17}[/tex] and [tex]\frac{14}{15}[/tex]?

Answer :

To find the least common denominator (LCD) of the fractions [tex]\(\frac{2}{17}\)[/tex] and [tex]\(\frac{14}{15}\)[/tex], we need to determine the smallest common multiple of their denominators, 17 and 15.

Here’s how we find it:

1. List the multiples of each denominator:

- Multiples of 17: [tex]\(17, 34, 51, 68, 85, 102, 119, 136, 153, 170, 187, 204, 221, 238, 255, \ldots\)[/tex]
- Multiples of 15: [tex]\(15, 30, 45, 60, 75, 90, 105, 120, 135, 150, 165, 180, 195, 210, 225, 240, 255, \ldots\)[/tex]

2. Identify the smallest common multiple:

By comparing the lists of multiples from step 1, we can see that the smallest multiple both lists share is 255.

Thus, the least common denominator of the fractions [tex]\(\frac{2}{17}\)[/tex] and [tex]\(\frac{14}{15}\)[/tex] is 255.