Question

PYTHON

In mathematics, the Greatest Common Divisor (GCD) of two integers is the largest positive integer that divides the two numbers without a remainder. For example, the GCD of 8 and 12 is 4. Steps to calculate the GCD of two positive integers a,b using the Binary method is given below: Input: a, b integers If a<=0 or b<=0, then Return 0 Else, d = 0 while a and b are both even do a = a/2 b = b/2 d = d + 1 while a ≠ b do If a%2== 0, then a = a/2 Else If b%2==0, then b = b/2 Else If a > b, then a = (a – b)/2 Else b = (b – a)/2 g = a Return g × 2^d Par(A): Write a function called findGCD that takes two positive integers a, b as parameters and, then calculates and returns the GCD of a, b using the Binary method given above. Part(B): The Least Common Multiple (LCM) of two integers a and b is the smallest positive integer that is divisible by both a and b and can be calculated using the following formula. LCM(a,b)= |ab|/(GCD(a,b)) where, |ab|= Absolute value of a*b GCD(a,b) = Greatest common divisor of a,b Part(C): Let a be any element from the listA and b be any element from the listB. (Note: listA and listB are taken from user) Write a user interface which calculates and displays the Greatest common divisor and Least Common Multiple of each possible pair of elements (a, b) from the two lists.

Answer 1

 from tkinter import * top = Tk() resultStr= StringVar() resultStr.set("Enter Numbers and Click the Button") number1Label = Label (text="First Number") number1Label.pack() number1Box = Entry() number1Box.pack() number2Label = Label (text="Second Number") number2Label.pack() number2Box = Entry() number2Box.pack() resultLabel = Label(textvariable=resultStr) resultLabel.pack() def findGCD(a,b): if a<=0 or b<=0 : return 0 d=0 while a%2==0 and b%2==0: a=a//2 b=b//2 d=d+1 while a!=b: if a%2==0: a=a//2 elif b%2==0: b=b//2 elif a>b: a=(a-b)//2 g=b else: b=(b-a)//2 g=a return g*(2**d) def fun(): no1 = int(number1Box.get()) no2 = int(number2Box.get()) no3 = findGCD(no1,no2) resultStr.set( "The GCD is "+str(no3)) but = Button(text="GCD", command=fun) but.pack() top.mainloop()

from tkinter import *

top = Tk()

resultStr= StringVar()
resultStr.set("Enter Numbers and Click the Button")
number1Label = Label (text="First Number")
number1Label.pack()
number1Box = Entry()
number1Box.pack()

number2Label = Label (text="Second Number")
number2Label.pack()
number2Box = Entry()
number2Box.pack()

resultLabel = Label(textvariable=resultStr)
resultLabel.pack()

def findGCD(a,b):
if a<=0 or b<=0 :
return 0
d=0
while a%2==0 and b%2==0:
a=a//2
b=b//2
d=d+1
while a!=b:
if a%2==0:
a=a//2
elif b%2==0:
b=b//2
elif a>b:
a=(a-b)//2
g=b
else:
b=(b-a)//2
g=a
  
return g*(2**d)

def fun():
no1 = int(number1Box.get())
no2 = int(number2Box.get())
no3 = findGCD(no1,no2)
resultStr.set( "The GCD is "+str(no3))
but = Button(text="GCD", command=fun)
but.pack()

top.mainloop()