To find the least common denominator (LCD) for the fractions [tex]\(\frac{1}{3} \text { and } \frac{4}{5}\)[/tex], follow these steps:
1. Identify the denominators: The denominators of the fractions are 3 and 5.
2. Find the least common multiple (LCM) of the denominators:
- List the multiples of each denominator.
- For 3: [tex]\(3, 6, 9, 12, 15, \ldots\)[/tex]
- For 5: [tex]\(5, 10, 15, 20, 25, \ldots\)[/tex]
- Identify the smallest multiple that is common to both lists.
3. Determine the least common multiple:
- From the lists above, the smallest common multiple between 3 and 5 is 15.
4. Confirm the least common denominator:
- Since the least common multiple of 3 and 5 is 15, the least common denominator of [tex]\(\frac{1}{3} \text { and } \frac{4}{5}\)[/tex] is also 15.
Thus, the least common denominator (LCD) for the fractions [tex]\(\frac{1}{3}\)[/tex] and [tex]\(\frac{4}{5}\)[/tex] is [tex]\(\boxed{15}\)[/tex].
