pyLeastCommonMultiple

# Find Least Common Multiple (LCM) from a list of integers
# Mike Kerry - Feb 2021 - acclivity2@gmail.com

def find_lcm(inlist):
    big = max(inlist)       # find the biggest integer from the provided list

    # Compute the product of all integers in the list.
    # This will provide the upper limit for our LCM search
    limit = 1
    for m in inlist:
        limit *= m

    # make "n" cycle through a range up to and including the limit, in steps of the biggest integer
    # This loop is guaranteed to find the LCM, even if the only Common Multiple equals "limit"
    for n in range(big, limit+1, big):
        for x in inlist:                # See if all integers in the input list divide cleanly into n
            if n % x:                   # if there was a remainder from the division ...
                break                   # ... then exit from this inner loop. "n" is not the LCM

        else:                           # If the inner loop completed successfully without "break" ...
            return n                    # ... then we have found the LCM
        # otherwise we continue executing the outer "for" loop to get the next value of "n"

    return None             # This statement will not be executed. It is only here to avoid Pycharm warnings


tests = [[6, 9], [4, 6, 8], [7, 11, 13], [2, 17, 5, 6, 9]]

for t in tests:
    lcm = find_lcm(t)
    print("The LCM of ", t, "is", lcm)


# Output:
# The LCM of  [6, 9] is 18
# The LCM of  [4, 6, 8] is 24
# The LCM of  [7, 11, 13] is 1001
# The LCM of  [2, 17, 5, 6, 9] is 1530