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