#-------------------------------------------------------------------------------

# Name: Problem 5

# Purpose: What is the smallest positive number that is evenly divisible by

# all of the numbers from 1 to 20?

#

# Author: Sebastián Torrente

#

# Created: 09/11/2012

# Comments: Let's analize first the properties of 2520 as the smallest number

# that can be divided by each of the numbers from 1 to 10 without

# any remainder.

# * 2520 = 2**3 * 3**2 * 5 * 7

# Ring any bell? It should, is the product of all the prime numbers

# below 10 each one at the higher possible power without surpassing

# 10.

# This give us the key to develop a generic solution for a number n:

# -Make a list of all the prime numbers under n

# -For each number find the highest exponential you can give it

#

# The solution can be calculated by hand without problem:

# - 2**4 * 3**2 * 5 * 7 * 11 * 13 * 17 * 19 = 232792560

# Let's see if we can make it via script too.

#-------------------------------------------------------------------------------

def smallEvenlyDiv(n):

"""Find the smallest positive number that is evenly divisible by all of the

numbers from 1 to n"""

# primList, listsol, prodsol = primes(n), [], 1

primList, listsol, prodsol = [2,3,5,7,11,13,17,19], [], 1 #Add a primes(n) function later

for number in primList:

power = 1

while number ** power <= n: power += 1

listsol.append(number ** (power - 1))

for number in listsol: prodsol *= number

return prodsol

if __name__ == '__main__':

print (smallEvenlyDiv(20))