When adding fractions with unlike denominators, we must change each fraction so they have the same denominator. Here's a simple example to start with.
1/2 + 1/4
To add these two fractions, we must get a denominator that is the same. This is called the common denominator. We can get a common denominator by multiplying the two denominators, in this problem it would be 2 x 4 = 8. But that is not the lowest common denominator, which is preferred when adding and subtracting fractions. To get the lowest common denominator, let's look at all the multiples of 2 and then the multiples of 4.
Multiples of 2 are
2, 4, 6, 8, 10, 12, …...
Multiples of 4 are
4, 8, 12, 16, 20, …..
The lowest common denominator is the smallest number that is the same in both sets of multiples. Notice the 4 is bold in each set. That is the lowest common denominator.
Now that we have the common denominator, we have to make ½ into an equivalent fraction with 4 as the denominator. . If we multiply the numerator and denominator by 2, we get 2/4.. Notice ¼ already has a denominator of 4, so we don't have to change this fraction in order to add. We now get...1/4 + 2/4 = 3/4