Write a program to find lcm and hcf of two numbers in python

Hey fellow coder! Today in this tutorial, we will learn how to compute the highest common factor (HCF) and Lowest common multiplier (LCM) using the python programming language.

Let us first understand what do we mean by HCF and LCM of two numbers if you are not familiar with these terms as of now.

Also read: Calculating Precision in Python — Classification Error Metric


What is Highest Common Factor (HCF)?

The highest common factor of two numbers is defined as the greatest common factor of the two numbers. For example, let’s consider two numbers 12 and 18.

The two numbers mentioned have the common factors as 2,3, and 6. The highest out of the three is 6. So in this case the HCF is 6.


What is Lowest Common Multiplier (LCM)?

The smallest/lowest common multiple of the two numbers is called the lowest common multiplier of the two numbers. For example, let’s consider the two numbers 12 and 18 again.

The multipliers of the two numbers can be 36, 72, 108, and so on. But we need the lowest common multipliers so the LCM of 12 and 18 will be 36.


Calculate HCF and LCM in Python

Let’s get right into implementing HCF and LCM in Python code.

1. Finding HCF of two numbers

a = int(input("Enter the first number: "))
b = int(input("Enter the second number: "))

HCF = 1

for i in range(2,a+1):
    if(a%i==0 and b%i==0):
        HCF = i

print("First Number is: ",a)
print("Second Number is: ",b)
print("HCF of the numbers is: ",HCF)

Let us pass two numbers as input and see what our results come out to be.

First Number is:  12
Second Number is:  18
HCF of the numbers is:  6

2. Finding LCM of two numbers

After we have computed the HCF of the two numbers, finding the LCM is not a tough task. LCM is simply equal to the product of the number divided by the HCF of the numbers.

a = int(input("Enter the first number: "))
b = int(input("Enter the second number: "))

HCF = 1

for i in range(2,a+1):
    if(a%i==0 and b%i==0):
        HCF = i

print("First Number is: ",a)
print("Second Number is: ",b)

LCM = int((a*b)/(HCF))
print("LCM of the two numbers is: ",LCM)

Let us pass the two numbers and see what the results turn out to be.

First Number is:  12
Second Number is:  18
LCM of the two numbers is:  36


Conclusion

I hope you are now clear with the computation of HCF and LCM of two numbers. And I guess you have also learned about the implementation of the same in the python programming language.

Thank you for reading! Happy learning! 😇


This article is created to cover some programs in Python, that find and prints LCM and HCF (GCD) of two numbers entered by user. Here are the list of programs:

  • Find LCM of Two Numbers
  • Find HCF (GCD) of Two Numbers
  • Find LCM and HCF of Two Numbers using Formula

How to Find LCM/HCF ?

If you don't know the thing used to find LCM or HCF (GCD), then you can refer to any of the following, whatever you required, to get everything about the topic:

  • How to Find LCM
  • How to Find HCF or GCD

Note - LCM stands for Least Common Multiple. Whereas HCF stands for Highest Common Factor.

Find LCM of Two Numbers

To find LCM of two numbers in Python, you have to ask from user to enter any two numbers, then find and print the LCM value as shown in the program given below. The question is, write a Python program to find LCM of two numbers. Here is its answer:

print("Enter Two Numbers: ")
numOne = int(input())
numTwo = int(input())

if numOne>numTwo:
    lcm = numOne
else:
    lcm = numTwo

while True:
    if lcm%numOne==0 and lcm%numTwo==0:
        break
    else:
        lcm = lcm + 1

print("\nLCM =", lcm)

Here is the initial output produced by this Python program:

Now supply inputs say 8 as first number, then press ENTER key, again enter a number say 20 as second number, now press ENTER key to find and print LCM value of these two numbers as shown in the snapshot given below:

Write a program to find lcm and hcf of two numbers in python

The dry run of above program with same user input as provided in sample run, goes like:

  • Initial values, numOne=8 (entered by user), numTwo=20 (entered by user)
  • Now the condition (of if) numOne>numTwo or 8>20 evaluates to be true, therefore program flow goes inside this if's body and the value of numOne (8) gets initialized to lcm. So lcm=8
  • If the condition was evaluated to be false, then program flow goes to else's body, instead of if's body
  • Now the condition (of while loop) True always evaluates to be true, therefore program flow goes inside the loop
  • And the first condition of if, that is lcm%numOne==0 or 8%8==0 evaluates to be true, therefore the second condition also gets evaluated. So the condition lcm%numTwo==0 or 8%20==0 evaluates to be false, therefore program flow goes to else's body and the value of lcm gets incremented by 1. So lcm=9
  • Since the condition of while loop always evaluates to be true, therefore this process continues, until both the condition of if evaluates to be true
  • That is, when both the condition of if evaluates to be true, then program flow goes inside its body and using break, the execution of while loop gets ended
  • And after exiting from the loop, I've printed the value of lcm as LCM value of given two numbers
  • So when the value of lcm becomes equal to 40, then the condition lcm%numOne==0 or 40%8==0 or 0==0 evaluates to be true, and the second condition lcm%numTwo==0 or 40%20==0 or 0==0 also evaluates to be true, therefore program flow goes inside the if's body and using break keyword, program flow goes out of the while loop
  • In this way, the LCM of two numbers gets calculated

Modified Version of Previous Program

This is the modified version of previous program. This program uses end to skip inserting an automatic newline using print(). The str() converts any type of value to a string type. The try-except is used to handle and print error message, when user enters non-integer values.

print("Enter Two Numbers: ", end="")
try:
    nOne = int(input())
    try:
        nTwo = int(input())
        if nOne > nTwo:
            lcm = nOne
        else:
            lcm = nTwo
        while True:
            if lcm % nOne == 0 and lcm % nTwo == 0:
                break
            else:
                lcm = lcm + 1
        print("\nLCM (" + str(nOne) + ", " + str(nTwo)+") = ", lcm)
    except ValueError:
        print("\nInvalid Input!")
except ValueError:
    print("\nInvalid Input!")

Here is its sample run with user input, 23 and 4 as two numbers:

Find HCF (GCD) of Two Numbers

This program is created to find and print the value of HCF or GCD of two numbers entered by user at run-time:

print("Enter Two Numbers: ", end="")
no = int(input())
nt = int(input())

if no>nt:
    hcf = no
else:
    hcf = nt

while True:
    if no%hcf==0 and nt%hcf==0:
        break
    else:
        hcf = hcf - 1

print("\nHCF (" + str(no) + ", " + str(nt) + ") = ", hcf)

Here is its sample run with 10 and 12 as two numbers entered by user:

Find LCM and HCF using Formula

This program uses formula to find and print LCM and HCF both in a single program:

print("Enter Two Numbers: ", end="")
no = int(input())
nt = int(input())

a = no
b = nt
while b!=0:
    temp = b
    b = a%b
    a = temp

hcf = a
lcm = int((no*nt)/hcf)

print("\nLCM (" + str(no) + ", " + str(nt) + ") = ", lcm)
print("HCF (" + str(no) + ", " + str(nt) + ") = ", hcf)

Here is its sample run with two numbers input as 7 and 56:

Same Program in Other Languages

  • Java Find HCF and LCM
  • C Find HCF and LCM
  • C++ Find HCF and LCM

Python Online Test


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How do you write a Python program to find the LCM of two numbers?

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.

How do you find the LCM using the math module in Python?

The math. lcm() function returns the least common multiple of the specified numbers..
If all the provided numbers are 0, it returns 0..
If no arguments are provided, it returns 1..
If a float or string parameter is provided, the math. lcm() method returns a TypeError ..

How do you find HCF and LCM?

The shortcut method to find both H.C.F. and L.C.M. is a division method..
Larger number/ Smaller Number..
The divisor of the above step / Remainder..
The divisor of step 2 / remainder. Keep doing this step till R = 0(Zero)..
The last step's divisor will be HCF..

How do you find the LCM in a for loop in Python?

Step 1:Initially, Get 2 Integer Inputs from the user using int(input()). Step 2:Find the greater number by using an If condition and assign it to the variable 'max'. Step 3:Within the while loop, Use an If condition to check whether the remainder of (max% a) and (max% b) equals to zero or not.

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