Question

find the least common denominator (lcd) of \\(\frac{1}{20}\\) and \\(\frac{11}{8}\\).

Explanation:

Step1: Factorize the denominators

Factorize \(20\) and \(8\) into their prime factors.
\(20 = 2\times2\times5=2^{2}\times5\)
\(8 = 2\times2\times2 = 2^{3}\)

Step2: Determine the LCD

The least common denominator (LCD) of two fractions is the least common multiple (LCM) of their denominators. To find the LCM, we take the highest power of each prime number present in the factorizations.
For the prime factor \(2\), the highest power is \(2^{3}\) (from the factorization of \(8\)).
For the prime factor \(5\), the highest power is \(5^{1}\) (from the factorization of \(20\)).
Then, \(LCM(20, 8)=2^{3}\times5\)
Calculate \(2^{3}\times5=8\times5 = 40\)

Answer:

\(40\)