Question

find the least common denominator for the group of fractions.\\(\frac{1}{10}, \frac{19}{60}, \frac{2}{5}, \frac{3}{11}\\)

Explanation:

Step1: Factor each denominator

Factor \(10\): \(10 = 2\times5\)
Factor \(60\): \(60=2^{2}\times3\times5\)
Factor \(5\): \(5 = 5\)
Factor \(11\): \(11=11\)

Step2: Identify the highest powers of all prime factors

For prime factor \(2\), the highest power is \(2^{2}\) (from \(60\)).
For prime factor \(3\), the highest power is \(3^{1}\) (from \(60\)).
For prime factor \(5\), the highest power is \(5^{1}\) (from \(10\), \(60\) or \(5\)).
For prime factor \(11\), the highest power is \(11^{1}\) (from \(11\)).

Step3: Calculate the least common denominator (LCD)

Multiply these highest powers together:
\(LCD=2^{2}\times3\times5\times11\)
\(= 4\times3\times5\times11\)
\(=12\times5\times11\)
\(=60\times11\)
\( = 660\)

Answer:

660