CMO 1998 Problem 1

Determine the number of real solutions $a$ to the equation: $$\left[\,\frac{1}{2} a\,\right]+\left[\,\frac{1}{3} a\,\right]+\left[\,\frac{1}{5} a\,\right] = a.$$ Here, if $x$ is a real number, then $[ x\,]$ denotes the greatest integer that is less than or equal to $x$ .