Q3 A B C

# part A


def commonFactor(n1, n2):
    l = []
    gcd = 1
    i = min(n1, n2)

    while(i >= 1):
        if(n1 % i == 0 and n2 % i == 0):
            gcd = i
            break
        i -= 1
    if(gcd == 1):
        l.append(1)
        print(l)
    for j in range(2, gcd + 1):
        if(gcd % j == 0):
            l.append(j)
    return l


# part B


def primeFactor(n):
    l = []
    i = 2
    start = n
    while(i <= n):
        if(n % i == 0):
            isprime = True
            j = 2
            while(j < i):
                if(i % j == 0):
                    isprime = False
                j += 1
            if(isprime == True):
                l.append(i)
                n /= i
        else:
            i += 1
    print(start, '=', l[0], end=" ")
    for j in range(1, len(l)):
        print('*', l[j], end=" ")
    print()
    return l


# part C


def LCM(numbers):
    mx = 0
    for i in numbers:
        if(mx < i):
            mx = i
    j = 1
    while(True):
        cur = mx * j
        cnt = 0
        for i in numbers:
            if(cur % i == 0):
                cnt += 1
        if(cnt == len(numbers)):
            return cur
            break
        j += 1


print("Part a")
print(commonFactor(12, 21))
print(commonFactor(60, 336))
print("==========")
print("Part b")
print(primeFactor(24))
print(primeFactor(31))
print(primeFactor(420))
print("==========")
print("Part c")
print(LCM([3, 4, 6, 10]))
print(LCM([2, 3, 8, 12, 16, 21]))
print("==========")