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Least Common Multiples

What is LCM?

Least Common Multiples(LCM) of two numbers is that multiples of all smallest common divisors until two integers become 1. The LCM is well know as lowest common multiple or smallest common multiple.

LCM Examples:

Two Numbers LCM Value
2, 2 2
2, 3 6
12, 24 24
9, 12 36

Mathematical Representation

We find the lcm of two numbers using mathematical representation

We find the lcm of three numbers using mathematical representation

C Program - LCM

Let us write a simple C program to find the LCM of two integers.

c-lcm.c
```#include <stdio.h>
int main()
{
int num1, num2, max;
printf("Enter two positive integers: ");
scanf("%d%d", &num1, &num2);
max = (num1 > num2) ? num1 : num2;
for(;;)
{
if(max % num1 == 0 && max % num2 == 0)
{
printf("LCM of %d and %d is %d ", num1, num2, max);
break;
}
max++;
}
return 0;
}```
```Enter two positive integers: 12 24
LCM of 12 and 24 is 24```

Note:

Here we make use of infinite for loop. Clearly first we will find the maximum of two integer. say 2 and 3 then max = 3. if two numbers are not divisible to max, then we will increase the max number count by 1 and we will check again. The same process is repeated over and over again until two numbers are divisible to max. Once two numbers are divisible to max, just return the max number.

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