You are actually trying to find the least common multiple of 480 and 576. The LCM is the product of the highest occurring primes in the prime factorization of both numbers...
480=2*2*2*2*2*3*5, 576=2*2*2*2*2*2*3*3 so the least common multiple is:
2*2*2*2*2*2*3*3*5 which is equal to:
2^6(3^2)5=2880 now to find n:
480n=2880
n=2880/480
n=6