How to find LCM in python

To find the LCM of two numbers, we start by writing an inequality with a on the LHS and b on the RHS. Then, we prime factor both sides. Last, we turn this expression into an equality by adding factors until both sides read the same. The product of all prime factors is the LCM.

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

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

# 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.

# 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.