Project Euler 5

题目

Smallest multiple

\(2520\) 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 \(20\)?

解决方案

根据定义，所求的值为\(1\sim20\)中间的所有数的最小公倍数\(\text{lcm}\)。

求多个数的\(\text{lcm}\)和求多个数的最大公因数\(\gcd\)做法一样，都是两两按顺序求。

使用了gmpy2库中的lcm方法，以后将封装到tools工具包中。

代码

from gmpy2 import lcm

N = 20
ans = 1
for i in range(1, 21):
    ans = lcm(ans, i)
print(ans)