Why 'NoneType' is returned in Python?

Question

I have a code that basically solves one of the problem in Project Euler and aims to find out LCM of first 20 natural numbers.

def GCD(a, b):              #Euclid's algorithim
    if (b == 0):
        return a
    else:
        GCD(b, a % b)

def LCM(a, b):             #LCM(a,b) = a*b/GCD(a,b)
    x = GCD(a, b)
    return ((a * b)/x)

def RFIND(a, b):
    if (b == 20):
        return a
    else:
        RFIND(LCM(a, b), b + 1)

print RFIND(2, 1)

But I face an error while running it.

    return ((a * b)/x)
TypeError: unsupported operand type(s) for /: 'int' and 'NoneType'

May I know Why?

Answer 1

Try

def GCD(a, b):              #Euclid's algorithim
    if (b == 0):
        return a
    else:
        return GCD(b, a % b)

You have to return the value returned by the recursive call. RFIND has a similar problem.

Answer 2

You've implemented your recursion incorrectly.

def GCD(a, b):              #Euclid's algorithim
 ...
        return GCD(b, a % b)

def RFIND(a, b):
 ...
        return RFIND(LCM(a, b), b + 1)