Let's say that and .

Then . Since m has at least one factor of 2, b must be an integer having a factor of 2 and must have a factor of 8. Since m has at least one factor of 3, a must be an integer having a factor of 3 and must have a factor of 9. The smallest possible value for m, then must be 8(9)= 72. Check: and which is NOT a perfect cube, 8 is but 3 is not. In order to maintain the "1/2 of the number is a perfect square" we must multiply by squares: comes to mind!

If m= 9(72)= 648, then m/2= 648/2= 324= .

m/3= 648/3= 216= .