To find the total of m+n+k, we first need to find the prime factorization of 30!.

First, let's find the powers of 2 in 30!:
30/2 = 15
15/2 = 7
7/2 = 3
3/2 = 1

So, the power of 2 in 30! is 15 + 7 + 3 + 1 = 26

Next, let's find the powers of 5 in 30!:
30/5 = 6
6/5 = 1

So, the power of 5 in 30! is 6 + 1 = 7

Finally, let's find the powers of 7 in 30!:
30/7 = 4
4/7 = 0

So, the power of 7 in 30! is 4

Therefore, 30! = (2^26) x (5^7) x (7^4)

So, m + n + k = 26 + 7 + 4 = 37

Therefore, m + n + k = 37