Dropping rows of matrix whose 3rd element is smaller than a number

I have an M X N matrix, I want to drop/delete all the rows whose 3rd element is less than 10^6, how I do I do it?

I tried putting conditional statement inside Drop command, and Pick command but so far I have only managed to get errors.

m = {{1, 2, 3}, {3, 2, 10^8}, {4, 1, 5}, {10, 20, 10^10}};

In[5]:= Select[m, #[[3]] > 10^6 &]

Out[5]= {{3, 2, 100000000}, {10, 20, 10000000000}}