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We have to rewrite the following fractions

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with fraction with least common denominator

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So LCD of the 2 fractions is going to be the LCM

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of both of these denominators over here.

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and if we can make this as common denominators

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we can add the two fractions

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First let us find the LCM,

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let me write it out LCD of 8 & 6

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is going to be the LCM of 8 & 6

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and a couple of ways to think about the LCM

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you could really take the multiples of 8 & 6

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and see what their smallest common multiple is.

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Multiples of 6 - 6,12,18,24,30... i can keep going

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and the multiples of 8 are 8,16,24,. looks like

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we are done. I have found a common multiple

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it is the smallest multiple they have other

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common multiples like 48,72 and we can go on

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but this is their smallest common multiple

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So it is 24. Another way to find the LCM is

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take the prime factorization of 6 - 2x3

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and the LCM of 6 must have one 2 & one 3

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what is the prime factorization of 8 is 2x2x2.

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Inorder to be divisible by 8 we need to have three 2's

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in the prime factorization. To be divisible by 6

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we need to have 2,3 and to be divisible by 8 we need

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three 2's, we have only one 2 so we add a couple more

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so thsi is now divisible by 6 & 8

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So 2x2x2x3 = 24. So LCM of 8 & 6

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which is the LCD also is 24

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So we want to write each of this fractions as

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24 as their denominator.

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So lets start with 2/8, i want to write that as / 24

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so get the denominator as 24,

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we need to multiply the denominator by 3

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inorder not to change the fraction, we need to

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multiply the numerator also by the same number

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so we will multiply numerator by 3 ; 2x3=6

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so 2/8 = 6/24

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2/8 x 3/3 = 6/24

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and lets do the same things with 5/6

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5/6 = / 24, i will do it in a different colour, blue

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to get the denominator from 6 to 24, we need

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to multiply by 4, so we need to multiply

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numerator also by 4 so 5x4 = 20

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5/6 = 20/24

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so we have written both the fractions with common denominator

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So we are done