We have to rewrite the following fractions
with fraction with least common denominator
So LCD of the 2 fractions is going to be the LCM
of both of these denominators over here.
and if we can make this as common denominators
we can add the two fractions
First let us find the LCM,
let me write it out LCD of 8 & 6
is going to be the LCM of 8 & 6
and a couple of ways to think about the LCM
you could really take the multiples of 8 & 6
and see what their smallest common multiple is.
Multiples of 6 - 6,12,18,24,30... i can keep going
and the multiples of 8 are 8,16,24,. looks like
we are done. I have found a common multiple
it is the smallest multiple they have other
common multiples like 48,72 and we can go on
but this is their smallest common multiple
So it is 24. Another way to find the LCM is
take the prime factorization of 6 - 2x3
and the LCM of 6 must have one 2 & one 3
what is the prime factorization of 8 is 2x2x2.
Inorder to be divisible by 8 we need to have three 2's
in the prime factorization. To be divisible by 6
we need to have 2,3 and to be divisible by 8 we need
three 2's, we have only one 2 so we add a couple more
so thsi is now divisible by 6 & 8
So 2x2x2x3 = 24. So LCM of 8 & 6
which is the LCD also is 24
So we want to write each of this fractions as
24 as their denominator.
So lets start with 2/8, i want to write that as / 24
so get the denominator as 24,
we need to multiply the denominator by 3
inorder not to change the fraction, we need to
multiply the numerator also by the same number
so we will multiply numerator by 3 ; 2x3=6
so 2/8 = 6/24
2/8 x 3/3 = 6/24
and lets do the same things with 5/6
5/6 = / 24, i will do it in a different colour, blue
to get the denominator from 6 to 24, we need
to multiply by 4, so we need to multiply
numerator also by 4 so 5x4 = 20
5/6 = 20/24
so we have written both the fractions with common denominator
So we are done