We know that LCM is the lowest common multiple of the given numbers.
a = 23 x 3
b = 2 x 3 x 5
c = 3n x 5
LCM of a,b,c = 23 x 3n x 5
Since, LCM will consists of the highest power of the prime factors. So, the power of 3 in finding out the LCM will be n as both a and b have consists of only one 3 as one of their prime factors.
Now, comparing the LCM obtained above by the given LCM, we get,
n = 2