Optimizing Python code for Project Euler #5 (LCM of all numbers from 1 to 20)

Question

This is my solution for the 5th problem of Project Euler, which asks for the least common multiples of the numbers from 1 to 20 (inclusive). Is there any way to improve the while loop conditional instead of using the sum?

table = range(1, 21)
result = 1
pf = 2
while sum(table) > len(table):
 flag = False
 for x, y in enumerate(table):
 if y % pf == 0:
 table[x] = y/pf 
 flag = True
 if flag:
 result *= pf
 else:
 pf += 1
print result

• tokland: are you interested in a functional solution without loops?
• Veritas: Nah I I know that it's possible to do the same using gcd and reduce, I just want to see how to better optimize this certain algorithm which is basically a pencil and paper algorithm designed for humams. Usually this ends when all elements become 1.

Answer 1

Your intent is to terminate the loop when all entries in table become 1. This

while sum(table) > len(table):

is a rather obscure way of expressing that intent. I suggest instead

while max(table) > 1:

or the more explicit and short-circuiting

while any(x > 1 for x in table):

Answer 2

Use a constant. It's easier to understand when you want to go back and try a different value too.

Copying my answer from stack overflow, also changed things around since this is code review.

MAX_FACTOR = 20 #The largest divisor we want to be able to divide by
#should have a general outline of the algorithm here
table = range(1,MAX_FACTOR + 1)
result = 1 #final result is stored here
currentFactor = 2 #what we're currently trying to divide by
while currentFactor <= MAX_FACTOR:
 isDivisor = False #is the currentFactor a divisor
 for x,y in enumerate(table):
 if y % currentFactor == 0:
 table[x] = y/currentFactor 
 isDivisor = True
 if isDivisor:
 result *= currentFactor
 else:
 currentFactor += 1
print result