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Find the least common denominator for these fractions. Enter your answer in the space provided.

[tex]\[ \frac{4}{6} \text{ and } \frac{1}{9} \][/tex]

Sagot :

GinnyAnswer
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.
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