Find the smallest positive integer n such that n has exactly 144 distinct positive divisors and there are 10 consecutive integers among them (Note: 1 and n are both divisors of n)

I haven't checked it yet, but I'm leaning towards

(2^3 )* (3^3) * (5^2) * (7^2).

264600

It has 144 divisors, including 1,2,3,4,5,6,7,8,9,10