How to get GCD and LCM of a range of numbers efficiently?

Question

I currently use this code to find gcd and lcm

def gcd(a, b):
    while b != 0:
        a, b = b, a%b
    return a

def lcm(a, b):
    result = a*b/gcd(a,b)
    return result

But what if I want to do this for a list of numbers e.g. [4,5,7,1,5,7,10,1,16,24] etc? Am I constrained to loops?

Answer 1

As mentioned by Chris J this SO question provides the algorithm. Here is a python version of the answer that uses the reduce built-in and the fractions module that has been around since version 2.6.

import fractions

def gcd(*values):
    return reduce(fractions.gcd, values)

Answer 2

from fractions import gcd
def lcm(a, b):
    return (a * b) // gcd(a, b)

Answer 3

You could use a recursive technique:

def gcd(a, b):
   if b == 0:
      return a
   else:
      return gcd(b, a%b)

Store all your GCD values in a hash map. So, when it does the recursive step, it first accesses the hash map to see if the GCD of the smaller numbers has already been computed, which will save a lot of time if you were doing this for a large range of inputs.