This question comes from ch.7.3 titled :Adding and subtracting rational Expressions with the same denominator and least common denominator.

## What is the LCD of 1/10x^4 and 4/5x

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# 2 Answers

1/(10x

^{4}) + 4/5xLike any fraction, you can only add or subtract two rational expressions if they have the same denominator. To find the LCD, you have to do a "prime factorization", factoring each denominator down to its prime numbers.

10x

^{4}= 2*5*x^{4}5x = 5*x

The LCD includes each unique prime factor. If a factor appears in more than one denominator, then choose the factor with the highest power. So for the above case, the unique prime factors are 2, 5, and x

^{4}:LCD = 2*5*x

^{4}= 10x^{4}To add then, we must change the denominator of the second expression to 10x

^{4}by multiplying it by the prime factors of the LCD it is missing, which is 2*x^{3}:1/(10x

^{4}) + (4/5x)(2x^{3}/2x^{3}) = 1/(10x^{4}) + (8x^{3})/(10x^{4}) = (1 + 8x^{3})/10x^{4}# Comments

I like your answer! Wendy, Philip is correct.

LCM of 2 or more numbers with the highest exponents= product of the common factors with highest exponents ( 1)

You know that by Fundamental laws of arithmetic every composite number is uniquely equal to the product of its prime factors

Take 2 numbers 36 , 24 ,using statement (1)

36 = 2

^{2}. 3^{2} 24 = 2

^{3}. 3 LCM ( 24, 36) = 2

^{3}. 3^{2}= 8 . ( 9) = 72 ( 2) If we take A = a

^{2}b^{2 }, and B = a^{3}. b LCM ( A , B ) = a

^{3}b^{2 }, where 36, 24 is a case where a =2 and b=3 Relation (1) implies that lowest number that divides both 36, 24 into it is 72

then

GCF - greatest Common factor is the greatest factor that both numbers can be divided by it.

it is the product of the common factor with the lowest exponent.

GCF ( 24, 36) = 4 . 3 = 12

So : LCM ( A, B ) = A. B / GCF ( A, B)

LCM ( 24, 36) = (24 . 36 ) / 12 = 72.

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