def is_prime(x, primes):
for p in primes:
if x % p == 0:
return False
return True
assert is_prime(3, [2])
assert not is_prime(4, [2, 3])
def smallest_common_multiple_of_all_numbers_up_to(x):
if x == 1:
return 1
y = 1
primes = []
for i in range(2, x + 1):
if is_prime(i, primes):
primes.append(i)
y *= i
continue
if y % i == 0:
continue
for p in primes:
if (y * p) % i == 0:
y *= p
break
return y
assert smallest_common_multiple_of_all_numbers_up_to(3) == 6
assert smallest_common_multiple_of_all_numbers_up_to(10) == 2520
print smallest_common_multiple_of_all_numbers_up_to(20)

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