Question

I need to find the LCD of fractions 3/4 + 6/7 and how to solve

Answer 1

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

`(3)/(4)=(3\cdot 7)/(4\cdot 7)=(21)/(28),\quad (6)/(7)=(6\cdot 4)/(7\cdot 4)=(24)/(28)`

So, the sum becomes

`(3)/(4)+(6)/(7)=(21)/(28)+(24)/(28)=(21+24)/(28)=(45)/(28)`

In fact, when two fractions have the same denominator, you can directly sum their numerators.