Hi Drdj,

Firstly lets observe the numbers

$\displaystyle 12 = 2^2.3$

$\displaystyle 45 = 3^2.5$

$\displaystyle 720 = 2^4.3^2.5$

so we observe that the LCM lacks a term that supplies $\displaystyle 2^4$ i.e if had taken the LCM of just 12,45 we would have ended up in $\displaystyle 180 = 2^2.3^2.5$

so the least value of x = 16 in that case we have all the factors we would need.

Now other feasible values of x are those that have $\displaystyle 2^4$ along with other factors like $\displaystyle 48 = 2^4.3$, $\displaystyle 90 = 2^4.5$,....,and last(and definitely not the least

) 720 itself so the maximum values of x = 720.

Kalyan.