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