Thread: 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

It's not on the list, but I would choose x = 36 (with y = 12 and z = 6). I think that gives a correct result.

Note that you can simplify the LHS to xyz