в чем проблема?
package com.javarush.task.task14.task1420;
import java.io.BufferedReader;
import java.io.InputStreamReader;
/*
НОД
*/
public class Solution {
public static void main(String[] args) throws Exception {
BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
int first = Integer.parseInt(reader.readLine());
int second = Integer.parseInt(reader.readLine());
if (first < 1 || second < 1) {
throw new IllegalArgumentException();
}
while (first !=0 && second !=0) {
if (first>second){
first = first % second;}
else if (first<second) {
second = second % first;
}
}
System.out.println(first+second);
}
}