HGFEDC * H   33894534 * 17       GGGGGG6  576207078

-------------------

def base2base(n,a,b):
    """ input n which is a string of the number to be changed
    'a' is an integer representing the current base
    to be changed to base b
    """
    def dec2base(i,base):
        """ INPUT integer in base 10, return string
        of Base base equivalent. """
        convertString = '0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ'
        if i < base:
            return convertString[i]
        else:
            return dec2base(i//base,base) + convertString[i%base]
    if a == 10:
        return dec2base(int(n),b)
    if b == 10:
        return int(str(n),a)
    elif b != 10:
        return base2base(int(str(n),a),10,b)


first6 = 18**5
last6 = 18**6 - 1
first7 = 18**6
last7 = 18**7 - 1


smallest = []
largest = []
smallFound = False
largeFound = False
for x in  range(first6, last6 + 1):
    if smallFound:
        break
    for m in range(2,18):
        p = x*m
        if p < first7:
            continue
        if p > last7:
            break
        p18 = base2base(p,10,18)
        if len(set(p18)) != 2:
            continue
        a = sorted(list(set(p18)))[0]
        b = sorted(list(set(p18)))[1]
        if abs( p18.count(a) -  p18.count(b)  ) != 5:
            continue
        print(p18, '=', base2base(m,10,18),'*', base2base(x,10,18))
        smallest.append([p, p18, m, base2base(m,10,18), x, base2base(x,10,18)])
        smallFound = True
        break


for x in  range(last6, first6 - 1, -1): # Reverse order
    if largeFound:
        break
    for m in range(2,18):
        p = x*m
        if p < first7:
            continue
        if p > last7:
            break
        p18 = base2base(p,10,18)
        if len(set(p18)) != 2:
            continue
        a = sorted(list(set(p18)))[0]
        b = sorted(list(set(p18)))[1]
        if abs( p18.count(a) -  p18.count(b)  ) != 5:
            continue
        print(p18, '=', base2base(m,10,18),'*', base2base(x,10,18))
        largest.append([p, p18, m, base2base(m,10,18), x, base2base(x,10,18)])
        largeFound = True
        break

print(smallest)
print(largest)
   

111111B = H * 123457
GGGGGG6 = H * HGFEDC
[[36012953, '111111B', 17, 'H', 2118409, '123457']]
[[576207078, 'GGGGGG6', 17, 'H', 33894534, 'HGFEDC']]