How do you find the lowest common multiple 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.

Published at Aug 25, 2021

Least Common Multiple in Python

The Least Common Multiple (LCM) is also referred to as the Lowest Common Multiple (LCM) and Least Common Divisor (LCD). For two integers a and b, denoted LCM(a,b), the LCM is the smallest positive integer that is evenly divisible by both a and b. For example, LCM(2,3) = 6 and LCM(6,10) = 30.

The LCM of two or more numbers is the smallest number that is evenly divisible by all numbers in the set.

How to Find the LCM in Python

def lcm(x, y): 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

Example

f"The Least Common Multiple of {number_1} and {number_2} is is {lcm(int(number_1), int(number_2))}"

What does LCM mean in Python?

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.

How do you find the LCM of multiples?

How to Find LCM by Listing Multiples.
List the multiples of each number until at least one of the multiples appears on all lists..
Find the smallest number that is on all of the lists..
This number is the LCM..

How do you find HCF and LCM in Python?

Algorithm.
Initialize HCF = 1..
Run a loop in the iteration of (i) between [1, min(num1, num2)].
Note down the highest number that divides both num1 & num2..
If i satisfies (num1 % i == 0 && num2 % i == 0) then new value of HCF is i..
Use lcm formula :- (num1*num2) / hcf..
Print the output..