Lowest Common Multiplier and Greatest Common Divisor in Python

Lowest Common Multiplier (LCM) and Greatest Common Divisor (GCD) can be found for any list of numbers by this code. 
LCM x GCD = FACT(x1,x2,...xn)
Here, FACT(x1,x2,...xn) is the multiplication of the input arguments x1 to xn. I used the above equation to find the GCD by calculating LCM first. However, you can calculate GCD directly using Euclid's algorithm.

Code

def lcm(x,y):
    tmp=x
    while (tmp%y)!=0:
        tmp+=x
    return tmp

def lcmm(*args):
    return reduce(lcm,args)

def fact(args):
    if len(args) == 0:
        return 1
    else:
        return args[0] * fact(args[1:])

def gcd(args):
    return fact(args)/lcmm(*args)

args=range(1,11)
print args
print 'LCM:', lcmm(*args)
print 'GCD:', gcd(args)

Euclid's Algorithm

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

Question

Find the sequence of numbers whose remainder is one less than its divisor?
Eg. Consider N, N mod x = x - 1 for x in list 1 - 20. Find the sequence of N?

Ans. Find the LCM of list 1 - 20, then N = k * LCM - 1, where k is an integer.