At last! A Project Euler problem I didn't brute-force. This problem was a fairly straight-forward LCM problem. I just reused my `factorize`

function from before and implemented the algorithm to find LCM by prime factorization.

```
"""Solves Problem 5 of Project Euler."""
def factorize(to_factor):
"""Use trial division to factorize to_factor and return all the resulting \
factors."""
factors = []
divisor = 2
while (divisor < to_factor):
if not to_factor % divisor:
to_factor /= divisor
factors.append(divisor)
# Note we don't bump the divisor here; if we did, we'd have
# non-prime factors.
elif divisor == 2:
divisor += 1
else:
# Trivial optimization: skip even numbers that aren't 2.
divisor += 2
if not to_factor % divisor:
# Don't forget the last factor
factors.append(to_factor)
return factors
def lcm(numbers):
"""Finds the Least Common Multiple of numbers."""
highest_degree_factors = {}
for number in numbers:
degrees_by_factor = {}
for factor in factorize(number):
# Translate the raw list of factors into a dictionary of degrees
# keyed on the factor.
current_degree = degrees_by_factor.setdefault(factor, 0)
degrees_by_factor[factor] = 1 + current_degree
# Update the top-level dict so it really is tracking the highest
# degrees.
for k, v in degrees_by_factor.iteritems():
highest_degree_factors.setdefault(k, v)
if highest_degree_factors[k] < v:
highest_degree_factors[k] = v
running_product = 1
for factor, degree in highest_degree_factors.iteritems():
running_product *= factor ** degree
return running_product
if __name__ == '__main__':
print lcm(range(1,20))
```

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