Determine the Least Common Multiple (LCM) of the algebraic expressions $x^{2}y$ and $x{y}^3$.

To find the Least Common Multiple (LCM) of algebraic expressions involving variables, we take the highest power of each variable present in the expressions.
Given expressions:

1. $x^2{y}^1$
2. $x^1{y}^3$

* The highest power of $x$ between $x^2$ and $x^1$ is $x^2$.
* The highest power of $y$ between $y^1$ and $y^3$ is $y^3$.

Multiplying these highest powers gives the LCM:

$$\text{LCM}=x^2\times y^3=x^2{y}^3$$