The least common denominator of two fraction is the least common multiple of the two denominator.
The least common multiple of 4 and 7 is their product 28, because 4 and 7 have no common factor.
Now, we need to manipulate both fractions so that they have denominator 28. Recalling that you can multiply numerator and denominator of a fraction by the same number without affecting its value, we have
[tex]\dfrac{3}{4}=\dfrac{3\cdot 7}{4\cdot 7}=\dfrac{21}{28},\quad \dfrac{6}{7}=\dfrac{6\cdot 4}{7\cdot 4}=\dfrac{24}{28}[/tex]
So, the sum becomes
[tex]\dfrac{3}{4}+\dfrac{6}{7}=\dfrac{21}{28}+\dfrac{24}{28}=\dfrac{21+24}{28}=\dfrac{45}{28}[/tex]
In fact, when two fractions have the same denominator, you can directly sum their numerators.
