If $x$ is a prime number, the LCM of $x$ and $(x+1)$ is

Any two consecutive integers $x$ and $x+1$ are always coprime to each other, meaning their Highest Common Factor ($\text{HCF}$) is equal to $1$. This remains true regardless of whether $x$ is prime or composite.
For any two coprime integers, their Least Common Multiple ($\text{LCM}$) is strictly equal to their mathematical product:

$$\text{LCM}(x,x+1)=x(x+1)$$