LCM=product of highest occurring primes in the numbers prime factorization.
GCF=product of shared primes in the numbers prime factorization.
16=2*2*2*2
Since the GCF is 8 N and 16 share only 2*2*2
Since the LCM is 48 and 16 has 2*2*2*2 the other number has a factor of 3
So the other number is 2*2*2*3=24
N=24