Two positive integers $x$ and $y$ are chosen, and their GCD and LCM are found to be the following: $gcd(x,y)=2178=23^2{11}^2,$ and lcm$(x,y)=44823240=2^3{3}^{3}57^3{11}^2.$ a$)$ You are told that $x$lcm$(x,y).$ Given only this information, what is the largest possible value of $x?$