# Good number theroy question

• Jan 9th 2009, 01:10 PM
howareyou1
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
• Jan 10th 2009, 01:28 AM
Opalg
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.
• Jan 10th 2009, 01:35 AM
Moo
Note that you can simplify the LHS to xyz (Surprised)