# 2520 is the smallest number that can be divided by each of the numbers from 1 to 10 without any remainder. # What is the smallest positive number that is evenly divisible by all of the numbers from 1 to 20? */ # returns smallest multiple that is evenly divisible by all numbers from 1 - n # returns -1 if multiple does not exist def findSmallestMultiple(n): for i in range(n, factorial(n) + 1, n): if isMultiple(i, n): return i return -1 # checks every number between 1 and n to see if x is a multiple of every number # returns True if x is found to be a multiple of every number, and False if x is # found to not be a multiple of any number def isMultiple(x, n): for i in range(1, n): if x % i != 0: return False return True # returns the n factorial, or -1 if it does not exist def factorial(n): if n > 1: return n * factorial(n - 1) elif n >= 0: return 1 else: return -1 print (findSmallestMultiple(10)) # 2520 print (findSmallestMultiple(20))DOWNLOAD

If you're running Python 2.x, the code above will fail for the second call of the function because the for-loop range will "contain too many items".

In that case, use the code below (while-loop instead of for-loop). If you're running Python 3.x, the code above will work just fine.

# 2520 is the smallest number that can be divided by each of the numbers from 1 to 10 without any remainder. # What is the smallest positive number that is evenly divisible by all of the numbers from 1 to 20? */ # returns smallest multiple that is evenly divisible by all numbers from 1 - n # returns -1 if multiple does not exist # works up to n = 20 (long reaches maximum value for values > 20) */ def findSmallestMultiple(n): i = n while i < factorial(n): if isMultiple(i, n): return i i += n return -1 # checks every number between 1 and n to see if x is a multiple of every number # returns True if x is found to be a multiple of every number, and False if x is # found to not be a multiple of any number */ def isMultiple(x, n): for i in range(1, n): if x % i != 0: return False return True # returns the n factorial, or -1 if it does not exist def factorial(n): if n > 1: return n * factorial(n - 1) elif n >= 0: return 1 else: return -1 print (findSmallestMultiple(10)) # 2520 print (findSmallestMultiple(20))DOWNLOAD

Created: February 16, 2014

Completed in full by: Michael Yaworski