### What is GCD?

The greatest common divisor (gcd) of two or more integers is the largest positive integer that divides each of the integers. For example, the gcd of 8 and 12 is 4. It is also known as the greatest common factor (gcf), highest common factor (hcf), greatest common measure (gcm), or highest common divisor.

### What is LCM?

The least common multiple, lowest common multiple, or smallest common multiple of two integers a and b, usually denoted by LCM(a, b), is the smallest positive integer that is divisible by both a and b.

### What is LCD?

The lowest common denominator or least common denominator (abbreviated LCD) is the lowest common multiple of the denominators of a set of fractions.

Regarding our problem, we can make functions to calculate GCD and LCM.

```
func gcd(numerator: Int, denominator: Int) -> Int
{
if (numerator == 0) {
return denominator;
} else {
return gcd(numerator: denominator % numerator, denominator:numerator);
}
}
func lcm(numerator: Int, denominator: Int) -> Int {
return (numerator * denominator) / gcd(numerator: numerator, denominator: denominator);
}
let lcd = lcm(numerator: f1.denominator, denominator: f2.denominator)
//use it in further calculation
```

Now to add, multiply, divide or subtract, all we need to do is to pass the numerator and denominator.