SOLUTION: Determine the lowest common multiple of the following three terms: xy, x^2 and xy^3

We look at the number of factors of x in each:

xy contains a factor of x 1 time.
x2 contains a factor of x 2 times.
xy3 contains a factor of x 1 time.

Therefore the LCM must contain a factor of x the most number
of times that any one of them contains x as a factor, which is
2 times.

We look at the factors of y (if any) in each:

xy contains a factor of y 1 time.
x2 contains a factor of y no (0, zero) times.
xy3 contains a factor of y 3 times.
 
Therefore the LCD must contain a factor of y the most number
of times that any one of them contains y as a factor, which is
3 times.

So the LCM contains a factor of x 2 times and a factor of y
3 times:

Answer = LCM = 

Edwin