Answer :
To find the least common denominator (LCD) of the fractions [tex]\(\frac{3}{17}\)[/tex] and [tex]\(\frac{13}{15}\)[/tex], we need to determine the smallest common multiple of their denominators: 17 and 15.
Here are the steps to find the least common denominator:
1. List the Multiples: List the multiples of each number.
- Multiples of 17: 17, 34, 51, 68, 85, 102, 119, 136, 153, 170, ...
- Multiples of 15: 15, 30, 45, 60, 75, 90, 105, 120, 135, 150, ...
2. Find Common Multiples: Identify the multiples that are common to both lists.
- Checking these lists, we are searching for the smallest number that appears in both lists.
3. Determine the Least Common Multiple (LCM): The smallest number common to both lists is the least common multiple.
- In this case, the LCM of 17 and 15 is 255.
Thus, the least common denominator of [tex]\(\frac{3}{17}\)[/tex] and [tex]\(\frac{13}{15}\)[/tex] is 255.
Here are the steps to find the least common denominator:
1. List the Multiples: List the multiples of each number.
- Multiples of 17: 17, 34, 51, 68, 85, 102, 119, 136, 153, 170, ...
- Multiples of 15: 15, 30, 45, 60, 75, 90, 105, 120, 135, 150, ...
2. Find Common Multiples: Identify the multiples that are common to both lists.
- Checking these lists, we are searching for the smallest number that appears in both lists.
3. Determine the Least Common Multiple (LCM): The smallest number common to both lists is the least common multiple.
- In this case, the LCM of 17 and 15 is 255.
Thus, the least common denominator of [tex]\(\frac{3}{17}\)[/tex] and [tex]\(\frac{13}{15}\)[/tex] is 255.
