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.
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.
