证明对于每一个有理数a,都有一个最小的正整数n可以让na是一个整数

Question

原题：Prove that for every rational number a, there is a smallest positive integer n such that na is an integer(use the fact that any nonempty set of positive integers has a smalliest element)
求教！！！

Answer 1

所有非整数的有理数都可以表达为一个分数。那么这个最小的正整数n就是这个分数的分母。