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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