def problem5(n):
"""
Returns the smallest integer such that every m <= n divides it
"""
accounted_for = set([1])
result = 1
for i in generate_primes_sieve(n + 1):
# We iterate through all available numbers, accounting for the
# powers of all numbers we see. Our result need only take into account
# the highest power of any number we look at
if i not in accounted_for:
index = 0
while i ** (index + 1) <= n:
index += 1
accounted_for.add(i ** index)
result *= i ** index
return result
