Here we do not need to worry about lowest common denominators or least common multiples because the denominators are already the same. All we add here is the 1 plus 2 which equals 3. The denominator remains the same.
You can see here that the denominator has been changed to the least common multiple (LCM), this way we make it easier to add. We know that 2 and 3 (the denominators) go into 6 equally. Now that we have chosen 6 to be the LCM, we have to understand what number times 2 equals 6, which is 3. We then multiply 3 by the nominator and the denominator to make a a new form of the fraction which becomes 3/6; three over six,
1 X 3 = 3
2 X 3 = 6 = 3/6 (three over six)
The same is done with 1/3, 3 times 2 is 6. 6 is the new dominator and to make the new nominator we then must multiply the nominator also by 2.
1 X 2 = 2
3 X 2 = 6 = 2/6 (two over six)
Watch this video, it shows adding fractions examples of both with different and same denominators.