Compute the greatest common divisor and least common multiple of two integers in python

In this program, you'll learn to find the LCM of two numbers and display it.

To understand this example, you should have the knowledge of the following Python programming topics:

• Python while Loop
• Python Functions
• Python Function Arguments
• Python User-defined Functions

The least common multiple [L.C.M.] of two numbers is the smallest positive integer that is perfectly divisible by the two given numbers.

For example, the L.C.M. of 12 and 14 is 84.

Program to Compute LCM

# Python Program to find the L.C.M. of two input number

def compute_lcm[x, y]:

   # choose the greater number
   if x > y:
       greater = x
   else:
       greater = y

   while[True]:
       if[[greater % x == 0] and [greater % y == 0]]:
           lcm = greater
           break
       greater += 1

   return lcm

num1 = 54
num2 = 24

print["The L.C.M. is", compute_lcm[num1, num2]]

Output

The L.C.M. is 216

Note: To test this program, change the values of num1 and num2.

This program stores two number in num1 and num2 respectively. These numbers are passed to the compute_lcm[] function. The function returns the L.C.M of two numbers.

In the function, we first determine the greater of the two numbers since the L.C.M. can only be greater than or equal to the largest number. We then use an infinite while loop to go from that number and beyond.

In each iteration, we check if both the numbers perfectly divide our number. If so, we store the number as L.C.M. and break from the loop. Otherwise, the number is incremented by 1 and the loop continues.

The above program is slower to run. We can make it more efficient by using the fact that the product of two numbers is equal to the product of the least common multiple and greatest common divisor of those two numbers.

Number1 * Number2 = L.C.M. * G.C.D.

Here is a Python program to implement this.

Program to Compute LCM Using GCD

# Python program to find the L.C.M. of two input number

# This function computes GCD 
def compute_gcd[x, y]:

   while[y]:
       x, y = y, x % y
   return x

# This function computes LCM
def compute_lcm[x, y]:
   lcm = [x*y]//compute_gcd[x,y]
   return lcm

num1 = 54
num2 = 24 

print["The L.C.M. is", compute_lcm[num1, num2]]

The output of this program is the same as before. We have two functions compute_gcd[] and compute_lcm[]. We require G.C.D. of the numbers to calculate its L.C.M.

So, compute_lcm[] calls the function compute_gcd[] to accomplish this. G.C.D. of two numbers can be calculated efficiently using the Euclidean algorithm.

Click here to learn more about methods to calculate G.C.D in Python.

# python program to find LCM of two number using GCD

#input two numbers
n1 = int[input["Enter First number :"]]
n2 = int[input["Enter Second number :"]]
x = n1
y = n2
while[n2!=0]:
    t = n2
    n2 = n1 % n2
    n1 = t
gcd = n1
print["GCD of {0} and {1} = {2}".format[x,y,gcd]]
lcm = [x*y]/gcd
print["LCM of {0} and {1} = {2}".format[x,y,lcm]]

>> %Run gcdlcm.py
Enter First number :54
Enter Second number :24
GCD of 54 and 24 = 6
LCM of 54 and 24 = 216.0

>>> %Run gcdlcm.py
Enter First number :4
Enter Second number :6
GCD of 4 and 6 = 2
LCM of 4 and 6 = 12.0

>>> %Run gcdlcm.py
Enter First number :125
Enter Second number :25
GCD of 125 and 25 = 25
LCM of 125 and 25 = 125.0

How do you find LCM and gcd in python?

How do you find the greatest common divisor of two numbers in python?

How do you find the least common divisor in python?

How do you find the LCM of two numbers in python?