Find the least common denominator for these fractions.

[tex]
\frac{1}{3} \text{ and } \frac{4}{5}
[/tex]

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Answer: _______



Answer :

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].