Question

Find the least common denominator (LCD) of 9/8 and 3/20

Answer 1

In order to find the least common denominator, first let's factor each denominator in their prime factors:

`\begin{gathered} 8=2\cdot2\cdot2=2^3\\ \\ 20=2\cdot2\cdot5=2^2\cdot5 \end{gathered}`

The LCD is given by the product of each prime factor, in the greatest number of times they show up in a value (for example, the prime factor 2 appears 3 times in number 8 and 2 times in number 20, so we use 3 times):

`LCD=2^3\cdot5=8\cdot5=40`

Therefore the LCD is 40.