To find the least common denominator (LCD) of the fractions [tex]\(\frac{4}{6}\)[/tex] and [tex]\(\frac{1}{9}\)[/tex], follow these steps:
1. Identify the denominators of the fractions. In this case, the denominators are 6 and 9.
2. Determine the least common multiple (LCM) of these denominators. The LCM of two numbers is the smallest number that is a multiple of both.
3. Factor each denominator into its prime factors:
- [tex]\(6\)[/tex] can be factored into [tex]\(2 \times 3\)[/tex].
- [tex]\(9\)[/tex] can be factored into [tex]\(3 \times 3\)[/tex].
4. Identify the highest power of each prime number present in the factorizations:
- For the prime number 2, the highest power present is [tex]\(2^1\)[/tex] (from the factorization of 6).
- For the prime number 3, the highest power present is [tex]\(3^2\)[/tex] (from the factorization of 9).
5. Multiply these highest powers together to find the LCM:
[tex]\[
\text{LCM} = 2^1 \times 3^2 = 2 \times 9 = 18.
\][/tex]
Therefore, the least common denominator (LCD) of the fractions [tex]\(\frac{4}{6}\)[/tex] and [tex]\(\frac{1}{9}\)[/tex] is 18.
