Midterm Question 3

Question

Write a program that asks the user to enter two integers, then calculates and displays their greatest common divisor (GCD) and their Least common multiple (LCM).

寫一個輸入兩個整數 輸出它們的最大公因數程式

Hint: Use Euclidean Algorithm

使用歐幾里得演算法

LCM:

In arithmetic and number theory, the least common multiple, lowest common multiple, or smallest common multiple of two integers a and b, usually denoted by LCM(a, b), is the smallest positive integer that is divisible by both a and b.

What is the LCM of 4 and 6?

Multiples of 4 are:

4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, ...

and the multiples of 6 are:

6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, ...

Common multiples of 4 and 6 are simply the numbers that are in both lists:

12, 24, 36, 48, 60, 72, ....

So, from this list of the first few common multiples of the numbers 4 and 6, their least common multiple is 12.

 

Example input: 

12 28

Example output (first number is GCD, second number is LCM):

4 84

 

Answer 1

Hidden content!
*****  ***  *  ** 

int main(){

  * *  **  * ** *   *** * * *  a,b,i,max,min;

***    * *   *  ** *    * ***  **** ***   * ****   *  **
 * * *    *   * *  *  ****** *  *   *   * && i<=b;i++){
   ****   * ***     **  ** *** *     *    * ***     *  *    * && b%i==0)
 ** * *  *  ***** * **   * * *  **** *** ***** * ** *   ****** *         ***    *     
 ** *   *   **  *   ****   
* ** * *    ***** ** **       *  *   ",max);

   *  * * * *  *   ** **   * *  * *  ** *
  * ***  * ** **     *   ***  *** ** * * ** **  **  *



return 0;
}

Comments

Case 0: Correct output
Case 1: Correct output
Case 2: Correct output
Case 3: Correct output
Case 4: Correct output

Answer 2

Hidden content!
#include<stdio.h>
int main()
{
    *   *   * ********** ***   *  a,b,c;
 * *** **    *   ** *** ***  ***      * * **  *  *   *** *  *
 ** ** * * ***  ****       ** **     *
    {
*  **  **  *  *  *** * * *** **** ** * **   * * *      
***   * ** * *** * * *   ***   **  *  *  * **    **  
 **   ** **   * ***  ********* ***    ** *   *  ** **** * *   *** 
  *   * ***  *  * ***   *  ***   
****  ** **  *   ***  *********   ****** *** *  * *
 ***    * ** **  ** * ** *    0;

}

Comments

Case 0: Wrong output
Case 1: Wrong output
Case 2: Wrong output
Case 3: Wrong output
Case 4: Wrong output

Answer 3

Hidden content!
#include * *  * *   **  * 
int main()
{
* * *  ** *     ***  *****   * * *  n1, n2, i, gcd;

   * *  *  *  ** ******    **  * * ***    ** *  &n1, &n2);

**  ** *** ** * *** ** **   ***** i <= n1 * ** ** i <= n2; ++i)
 *** **    *   *********  * 
*  **    **   *** **   **  *  ****     ***   * *** **  *     * * *   * n2%i==0)
 **  ** ** *  **  **  *   *   **  * * ** *   **   * * **** = i;
 *  * **  **  * ** **** 
  * *   *    **  **   **   **    ** * * *  * * **** * * gcd);
      ** *  ***  ** ** *   ** 0;
}

Comments

Case 0: Wrong output
Case 1: Wrong output
Case 2: Wrong output
Case 3: Wrong output
Case 4: Wrong output

Answer 4

Hidden content!
#include <stdio.h>
int main()
{
    *    **** ** ** **    *   a,b,gcd,lcm;
 * **   **     *** *   *** *  *  **   *  %d",&a,&b);
***** ***     ***  **    * ***   (a%b!=0)
** ********     *  *  ***  *    
     * *** *   *****    * * *  **      *********  **  ** 
* *** * *      ***   ** ****** * ****** *****   ***     *  
**  *** *  *   * *  ***  * ** **  * *  * ***   *    * 
 **   * *** ** **  **     
*  * *   ** ***  * *      *  *  *** * *  ** 
** ****  ** ** *  ** *** *   **** * ***  %d",gcd,lcm);
***   *   *   *  **  *** * ** ** 0;
}

Comments

Case 0: Wrong output
Case 1: Wrong output
Case 2: Wrong output
Case 3: Wrong output
Case 4: Wrong output

Answer 5

Hidden content!
#include<stdio.h>
int main()
{
*** ** * * ***   **   ** *  a,b,a1,b1,remainder,LCM;
*****       ** *  ** ** *   *  *   *  %d",&a,&b);
      ***   *   **  ***   *   
*  **   * **    *    * *** *  ***** 
 *  * * ** *** ***   **  * *** *     *
**    * ****** **** ****    **
  * *** ** *****   ***   ** ****  ** ****** ********* **  *  *  * **  
* *    ** ********* **** **  ***     **** *****  *     *
 ****   ***  ******    **  *     *   **** *  * * *   * * *  ** * ** *
       * ** *** * *  ** *** 
     **    ** * *  **   ** * ** **
 ***  *     ** * *  ** * *** * ** ***  *   %d",a,LCM);
  ** **  *  * *      ***   ***   * 0;
}

Comments

Case 0: Correct output
Case 1: Correct output
Case 2: Correct output
Case 3: Correct output
Case 4: Correct output

Answer 6

Hidden content!
#include <stdio.h>
int main()
{
    int a,b,i,x,y,gcd,lcm=0;
   *  * * *     **  ***     ***  ** * * %d",&a,&b);
   * *   *    **  ** *  **     *  *  ***  **
****   *  ** * * **  *  **  *    * * ** *  ** **
  **  *     *  **  *******   ** *  *** * * *** * * * * * **   **  **
* * ***** * ** *** *** *  ***     * *  * ****  *  **  *** && y==0){
  * * ** ** * * * * ***   * ***  * ***   *       **  **  ** ***  ******   *  *   **
 ******* * ** * * *  *   ** **  **** *   ****
    }
 ***  * ** **      ** * * *
  ****  ****  * *    *** 
** *** **   *** * **          *******  **   **** ***   *** *
 * ** ***** *  *  * *  * ** *  *  **     *    * * ** *** 
 *  *  **** * ** **  **  *** * ****    **  ******    ** * ** && y==0){
 ** * ** * * ***   *  * *  ** *     *****   **** ***   ** ** * *** * *** *  *  * *
  **   ******* *  * **   ****** *      *** **  ***   ** ** ***   ** ****  *  *****  *  
 *  * * * ** *   ** **   *****   * *  *  **  **  *
*** ** **  **   ***  ***  * *** * ** * *  *   * *    * *   
    }
  ** * *  ** *       ** *** *** * *   %d",gcd,lcm);
 *****     *******    *   **  0;
}

Comments

Case 0: Correct output
Case 1: Correct output
Case 2: Correct output
Case 3: Correct output
Case 4: Correct output