Tag: LCM

Lets write a C program to find Least Common Multiple (LCM) of 2 integer numbers.

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Least Common Multiple(LCM): is the smallest positive integer that is perfectly divisible by the given integer values.

Logic to Find LCM of Two Numbers

We assign variable fact with a initial value of 1. While loop keeps executing until fact value is 0. We ask the user to enter 2 integer numbers. Now we find the biggest of these 2 numbers and store it inside variable lcm. We can even skip this step – in which case while loop has to execute more number of times. To optimize the code we find biggest of the 2 user input numbers and store it inside variable lcm – we do this because, we need to find a number which is perfectly divisible by both the user entered number, so obviously the number should be greater than or equal to the biggest number entered by the user.

Next, inside while loop we check if the value present in variable lcm is perfectly divisible by both num1 and num2. Once the condition is true, we display the result on to the console window and assign value 0 to variable fact. Once fact is 0, control exits while loop.

If the value of lcm is not perfectly divisible by both num1 and num2, then we increment the value of variable lcm by 1 and check for divisibility once again. We keep executing the while loop and keep incrementing the value of lcm by 1 until the value present in lcm is perfectly divisibile by value of num1 and num2.

Source Code: C Program to Find LCM of Two Numbers

 
#include < stdio.h >

int main()
{
    int num1, num2, lcm, fact =1;

    printf("Enter 2 numbers\n");
    scanf("%d%d", &num1, &num2);

    lcm = (num1 > num2) ? num1 : num2;

    while(fact)
    {
        if(lcm % num1 == 0 && lcm % num2 == 0)
        {
            printf("LCM of %d and %d is %d\n", num1, num2, lcm);
            fact = 0;
        }
        lcm++;
    }

    return 0;
}

Output 1:
Enter 2 numbers
24
60
LCM of 24 and 60 is 120

Output 2:
Enter 2 numbers
2
3
LCM of 2 and 3 is 6

C Program to Find LCM of Two Numbers

Explanation With Example

If 2 numbers are num1 = 2 and num2 = 3.
We find biggest of these two numbers and store it inside variable lcm.
So 3 is greater than 2, so lcm = 3.

Iteration 1
fact = 1;
lcm = 3;

lcm % num1 = 3 % 2 = 1 // not equal to 0
lcm % num2 = 3 % 3 = 0 // equal to 0

Increment value of lcm by 1. So lcm = 4.

Iteration 2
fact = 1;
lcm = 4;

lcm % num1 = 4 % 2 = 0 // equal to 0
lcm % num2 = 4 % 3 = 1 // not equal to 0

Increment value of lcm by 1. So lcm = 5.

Iteration 3
fact = 1;
lcm = 5;

lcm % num1 = 5 % 2 = 2 // not equal to 0
lcm % num2 = 5 % 3 = 1 // not equal to 0

Increment value of lcm by 1. So lcm = 6.

Iteration 3
fact = 1;
lcm = 6;

lcm % num1 = 6 % 2 = 0 // equal to 0
lcm % num2 = 6 % 3 = 0 // equal to 0

Since both the condition are true
i.e., lcm%num1 == 0 && lcm%num2 == 0

We printout the value of variable lcm i.e., 6 as the Least Common Multiple of numbers 2 and 3. Next we assign 0 to variable fact. Since fact is 0, control exits while loop.

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