Least common base function --will probably infinite-loop for inputs without an ideal answer

lcb.py

from itertools import combinations
from math import log, ceil


def common_bases(x: int, y: int) -> int:
    """
    Returns a list of all the bases common to x and y
    That is to say, all bases n such that n can be raised by an integer power to
    produce x or y
    The list returned is sorted in ascending order, and may be empty if there
    are no common bases
    """
    # try the nth root of x for n in {2..x-1}, and same for y
    # keep any which are integers
    x_roots = {round(x ** (1/xr)) for xr in range(2, x) if round(x ** (1/xr)) ** xr == x}
    y_roots = {round(y ** (1/yr)) for yr in range(2, y) if round(y ** (1/yr)) ** yr == y}
    # return the sorted intersection of the integer roots of x and y
    return list(sorted(x_roots.intersection(y_roots)))


def lcb(x: int, y: int) -> int:
    """
    Attempts to find the least common base to both x and y, that is to say,
    a number (t) that can be raised by some powers a,b to make x,y respectively
    """
    return common_bases(x, y)[:1]


def gcb(x: int, y: int) -> int:
    """
    Attempts to find the greatest common base to both x and y, that is to say,
    a number (t) that can be raised by some powers a,b to make x,y respectively
    """
    return common_bases(x, y)[-1:]


# find all common base pairs up to 1000
print('x,y,lcb,gcb')
for x, y in combinations(range(1, 1001), 2):
    l = lcb(x, y)
    g = gcb(x, y)
    if l and g:
        print('{},{},{},{}'.format(x, y, l[0], g[0]))