Answer:
The program written in Python is as follows
def GCD(num1, num2):
small = num1
if num1 > num2:
small = num2
for i in range(1, small+1):
if((num1 % i == 0) and (num2 % i == 0)):
gcd = i
print("The GCD is "+ str(gcd))
def LCM(num1,num2):
big = num2
if num1 > num2:
big = num1
while(True):
if((big % num1 == 0) and (big % num2 == 0)):
lcm = big
break
big = big+1
print("The LCM is "+ str(lcm))
print("Enter two numbers: ")
num1 = int(input(": "))
num2 = int(input(": "))
GCD(num1, num2)
LCM(num1, num2)
Explanation:
This line defines the GCD function
def GCD(num1, num2):
This line initializes variable small to num1
small = num1
This line checks if num2 is less than num1, if yes: num2 is assigned to variable small
<em> if num1 > num2:
</em>
<em> small = num2
</em>
The following iteration determines the GCD of num1 and num2
<em> for i in range(1, small+1):
</em>
<em> if((num1 % i == 0) and (num2 % i == 0)):
</em>
<em> gcd = i
</em>
This line prints the GCD
print("The GCD is "+ str(gcd))
This line defines the LCM function
def LCM(num1,num2):
This line initializes variable big to num2
big = num2
This line checks if num1 is greater than num2, if yes: num1 is assigned to variable big
<em> if num1 > num2:
</em>
<em> big = num1
</em>
The following iteration continues while the LCM has not been gotten.
while(True):
This if statement determines the LCM using modulo operator
<em> if((big % num1 == 0) and (big % num2 == 0)):
</em>
<em> lcm = big
</em>
<em> break
</em>
<em> big = big+1
</em>
This line prints the LCM of the two numbers
print("The LCM is "+ str(lcm))
The main starts here
This line prompts user for two numbers
print("Enter two numbers: ")
The next two lines get user inputs
num1 = int(input(": "))
num2 = int(input(": "))
This calls the GCD function
GCD(num1, num2)
This calls the LCM function
LCM(num1, num2)
<em></em>
<em>See attachment for more structured program</em>
