'===========================================================================
' Subject: SOLVING LCM AND GCD               Date: 10-28-95 (12:00)       
' Author:  The ABC Programmer                Code: QB, QBasic, PDS        
' Origin:  Computer Science Book           Packet: ALGOR.ABC
'===========================================================================
'==========================================
' Finding the Lowest(Least) Common Multiple
' and the Greatest Common Divisor
' Programmed by William Yu (10-28-1995)
'
' This program helps, where calculators
' can not compute the exact fractions.
'==========================================

DECLARE SUB FindLCM (Numbers(), Max, X)
DECLARE SUB FindGCD (Numbers(), Max, X)
DECLARE SUB AddFractionDemo (Numbers(), Max, Denominator)

DIM Numbers(10)

CLS
                       ' Keeping the numbers simple to avoid long waits
Numbers(1) = 28        ' You can modify/add/remove as you wish
Numbers(2) = 42        ' If you add or remove one or more numbers
Numbers(3) = 126       ' make sure you do the same for the AddFractionDemo
Numbers(4) = 98        ' Numerators()

Max = 4                ' Change this to correspond to Max Numbers()
                       '                       and Max Numerators()

PRINT "The LCM for"; : COLOR 15
FOR I = 1 TO Max
  PRINT Numbers(I);
NEXT I
COLOR 7: PRINT "is"; : COLOR 15

FindLCM Numbers(), Max, X
Denominator = X: PRINT X

COLOR 7: PRINT "The GCD for"; : COLOR 15
FOR I = 1 TO Max
  PRINT Numbers(I);
NEXT I
COLOR 7: PRINT "is"; : COLOR 15

FindGCD Numbers(), Max, X
PRINT X

AddFractionDemo Numbers(), Max, Denominator

SUB AddFractionDemo (Numbers(), Max, Denominator)

' Adding fractions using LCM as our Denominator
' Can you think of another way to add fractions?
' There is, but is not commonly used because it can be tedious doing by
' hand, and even on the computer it is quite slow.
' But the other way of adding fractions is to multiply all the denominators
' to get your grand total.  And then add your numerators.  Now that you
' have two great big numbers to work with, you find the GCD to reduce
' the fraction.  Try it, which one is faster?  Using LCM or GCD?
' Obviously GCD works best if you cannot find the LCM, but sometimes it
' will not work because the numbers are too large.  LCM is your best bet.

DIM Numerator(10), Fraction(2)

Numerator(1) = 22
Numerator(2) = 3
Numerator(3) = 35
Numerator(4) = 4

PRINT : PRINT "Add Fraction Demo:"; : COLOR 7: PRINT : PRINT
PRINT "      ";
FOR I = 1 TO Max
  PRINT USING "###"; Numerator(I); : PRINT "   ";
NEXT I
PRINT
PRINT "      ";
FOR I = 1 TO Max
  PRINT "---";
  COLOR 15: IF I <> Max THEN PRINT " + ";
  COLOR 7
NEXT I
PRINT "  = ----"
PRINT "      ";
FOR I = 1 TO Max
  PRINT USING "###"; Numbers(I); : PRINT "   ";
NEXT I

PRINT Denominator

' Next, we calculate the numerator

FOR I = 1 TO Max
  Numerator = Numerator + (Denominator / Numbers(I) * Numerator(I))
NEXT I
PRINT : PRINT "     "; Numerator
PRINT "      ----  =   Find GCD": PRINT "     "; Denominator

Fraction(1) = Numerator          ' Plug in the numbers
Fraction(2) = Denominator        ' to be reduced

FindGCD Fraction(), 2, X         ' Find the GCD to reduce the fraction

Numerator = Numerator / X        ' Divide by the GCD
Denominator = Denominator / X
PRINT : PRINT "     "; Numerator
PRINT "      ----  =   Divided by GCD": PRINT "     "; Denominator

I = 0
IF Numerator > Denominator THEN         ' Let's convert this to mixed
  DO                                    ' fraction
    I = I + 1
    Numerator = Numerator - Denominator
  LOOP UNTIL Numerator <= Denominator
END IF

' We are finally done!  Let's print the answer.

PRINT : PRINT "     "; Numerator: PRINT ; "   ";
IF I > 0 THEN PRINT I;  ELSE PRINT "   ";
PRINT "----  =   Answer": PRINT "     "; Denominator

END SUB

SUB FindGCD (Numbers(), Max, X)

HighestNumber = Numbers(1)
HoldX = 1
C = 1

FOR I = 2 TO Max
  IF Numbers(I) = Numbers(1) THEN C = C + 1
  IF Numbers(I) > HighestNumber THEN HighestNumber = Numbers(I) / 2
NEXT I

IF C = Max THEN X = Numbers(1): EXIT SUB

X = 2: I = 1

DO
  IF Numbers(I) MOD X THEN        ' Check for Remainder
    X = X + 1
    I = 1
  ELSE                            ' No remainder, passed
    I = I + 1
  END IF
  IF I = Max + 1 THEN HoldX = X: I = 1: X = X + 1
  IF X = HighestNumber + 1 THEN EXIT DO
LOOP

X = HoldX

END SUB

SUB FindLCM (Numbers(), Max, X)

X = Numbers(1): I = 1

DO
  IF INT(X / Numbers(I)) = X / Numbers(I) THEN   ' Are they really equal?
    IF I = Max THEN                              ' Last number checked is
      EXIT DO                                    ' equal, end do..loop
    ELSE
      I = I + 1                                  ' Equal, check next number
      IF I = Max + 1 THEN I = Max
    END IF
  ELSE                                           ' No they're not
    X = X + 1: I = 1                             ' Start from beginning
  END IF                                         ' Incr X (Slow)
LOOP

END SUB