Problem 5:Smallest multiple

原题地址：http://projecteuler.net/problem=5

Smallest multiple

Problem 5

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?

大意是：

2520是最小的能被1-10中每个数字整除的正整数。

最小的能被1-20中每个数整除的正整数是多少？

解法1：

1.列出20以内的质数，并求这些质数的小于20的最高次幂

2.再将这些质数的最高次幂的积相乘

python代码如下：

primelist = {2:0,3:0,5:0,7:0,11:0,13:0,17:0,19:0}

def setPrimelist():
  for x in primelist.keys():
     num = x
     while num*x < 20:
            primelist[x] += 1
            num *= x
     else:
        primelist[x] += 1

         
def minProduct():
    sum = 1
    for x in primelist.keys():
        sum *= x**primelist[x]
    
    return sum

if __name__ == '__main__':
    setPrimelist()
    print minProduct()

注：题目的中文翻译源自http://pe.spiritzhang.com