We have lcm(2, 3, 5) = 30, but none of 30/2 = 15, 30/3 = 10, nor 30/5 = 6 are divisible by 2, 3, and 5, respectively.
To account for this, take the square of 30, 30² = 900. Then 900/2 = 450, 900/3 = 300, and 900/5 = 180 are respectively divisible by 2, 3, and 5.
Multiply this by 2 to get a 4-digit number. It follows that [tex]\boxed{a=1800}[/tex].
