Freeing memory which has been allocated to an array of char pointers (strings). Do I have to free each string or just the "main" pointer?

I have a function that takes a pointer to a char ** and fills it with strings (an array of strings I guess). *list_of_strings* is allocated memory inside the function.

char * *list_of_strings = NULL;

/* list_of_strings malloc'd inside function */
fill_strings_with_stuff(&list_of strings);

use_list_for_something(list_of_strings);

/* Now how do I free it all? */

How would I go about freeing the memory after I've used the strings? If I call

free(list_of_strings);

won't that just free the actual pointers and not the memory each string itself was using? How do I completely free the memory

Just for clarity the function looks something like this:

fill_strings_with_stuff(char *** list)
{
    *list = malloc(AMOUNT);

    for (i = 0; i < SOMETHING; i++) {
        *(list + i) = malloc(LINE_LEN);
        *(list + i) = some_string_from_somewhere
    }

    /* ... */

}