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# Python Program to Find LCM and HCF (GCD) of Two Numbers

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:

**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:

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

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