Good number theroy question

Here was a very tough bonus question we had on our pre-calc final today

(x^3*y^3*z^3)**/**(gcf(x,y)*gcf(x,z)*gcf(y,z)*lcm(x,y)*lcm(x,z)*lcm( y,z))=(lcm(x,y)*lcm(x,z)*lcm(y,z))**/**(gcf(x,y,z))

sorry i dont know latex very well, but its two things set equal and watch out for the division signs

greatest common factor =gcf, so like gcf(2,4)=2. least common multiple = lcm, so lcm(2,3)=6

where x>y>z. Find the smallest possible value of x that satisfies this equation.

I experiemented with numbers and I guessed 150(i tried splitting up into its factors and creating other numbers from them)...i wasnt sure though. can anyone verify because I do not want to wait until next Friday to see what mny final grade might have been.

Thye choices were like 50, 60, 90, 150, or 180

Thanks