The smallest positive integer value of n for which 480n is a multiple of 576. find n

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

Dm me pls mike and