gistfile1.py

X = 233
Y = 456
Z = 787
TARGET = 10000000000

def gcd(x, y): # x >= y
    mod = x%y
    if mod == 0: return y
    return gcd(y, x%y)

def lcm(x, y):
    g = gcd(max(x,y), min(x,y))
    return x*y / g

MAX_X = min(lcm(Y, X)/X, lcm(Z, X)/X)
MAX_Y = lcm(Y, Z)/Y

def solve():
    tgt = TARGET
    _X = X
    _Y = Y
    _Z = Z
    min_result = tgt
    for num_xy in xrange(MAX_X + MAX_Y - 1):
        for x in xrange(num_xy):
            y = num_xy - x
            if (tgt - y*_Y - x*_X) % Z == 0:
                z = (tgt - y*_Y - x*_X) / Z
                result = x+y+z
                if result < min_result:
                    print x, y, z, x*_X+y*_Y+z*_Z
                    min_result = result
                    break
    return min_result

print solve()