最大公约数与最小公倍数

本例效果图:

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代码文件:

---

unit Unit1;

interface

uses
  Windows, Messages, SysUtils, Variants, Classes, Graphics, Controls, Forms,
  Dialogs, StdCtrls;

type
  TForm1 = class(TForm)
    Button1: TButton;
    Edit1: TEdit;
    Edit2: TEdit;
    procedure Button1Click(Sender: TObject);
  end;

var
  Form1: TForm1;

implementation

{$R *.dfm}

{求最大公约数
 算法: 假如 x > y, x mod y 取余数后,
 y 付给 x、余数付给 y,
 然后重复运算, 最后非 0 的余数就是最大公约数
}
function zdgys(x,y: Cardinal): Cardinal;
var
  n: Integer;
begin
  n := y;
  if x < y then
  begin
    y := x;
    x := n;
  end;

  while n > 0 do
  begin
    n := x mod y;
    x := y;
    if n > 0 then y := n;
  end;
  Result := y;
end;

{求最小公倍数
 算法: x * y div 它们的最大公约数
}
function zxgbs(x,y: Cardinal): Cardinal;
var
  m,n: Cardinal;
begin
  m := x * y;
  n := y;
  if x < y then
  begin
    y := x;
    x := n;
  end;

  while n > 0 do
  begin
    n := x mod y;
    x := y;
    if n > 0 then y := n;
  end;

  Result := m div y;
end;

{测试}
procedure TForm1.Button1Click(Sender: TObject);
const
  str = '%0:d 与 %1:d 的最大公约数是 %2:d'#13#10'%0:d 与 %1:d 的最小公倍数是 %3:d';
var
  x,y,a,b: Cardinal;
begin
  x := StrToIntDef(Edit1.Text, 1);
  y := StrToIntDef(Edit2.Text, 1);
  a := zdgys(x, y);
  b := zxgbs(x, y);
  ShowMessageFmt(str, [x,y,a,b]);
end;

end.

窗体文件:

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object Form1: TForm1
  Left = 0
  Top = 0
  Caption = 'Form1'
  ClientHeight = 160
  ClientWidth = 268
  Color = clBtnFace
  Font.Charset = DEFAULT_CHARSET
  Font.Color = clWindowText
  Font.Height = -11
  Font.Name = 'Tahoma'
  Font.Style = []
  OldCreateOrder = False
  PixelsPerInch = 96
  TextHeight = 13
  object Button1: TButton
    Left = 176
    Top = 14
    Width = 75
    Height = 25
    Caption = 'Button1'
    TabOrder = 0
    OnClick = Button1Click
  end
  object Edit1: TEdit
    Left = 17
    Top = 16
    Width = 64
    Height = 21
    TabOrder = 1
    Text = 'Edit1'
  end
  object Edit2: TEdit
    Left = 98
    Top = 16
    Width = 63
    Height = 21
    TabOrder = 2
    Text = 'Edit2'
  end
end