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 Post subject: GMAT Number Theory
PostPosted: Wed Apr 04, 2012 1:31 am 
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Joined: Sun May 30, 2010 3:15 am
Posts: 424
If n is a positive even integer, then what are the GCF and LCM of the expressions n² + 5n + 6 and n² + 3n + 2?

Solution:
Just as with numbers, you need to compare the factors.

n² + 5n + 6 = (n + 2)(n + 3)

n² + 3n + 2 = (n + 2)(n + 1)

(n + 2) is a common factor, while (n + 3) and (n + 1) are two consecutive odd integers. The GCF of two consecutive odd integers is 1, because if we divide (n + 3) by any factor of (n + 1), the remainder will be 2.

Therefore the GCF of n² + 5n + 6 and n² + 3n + 2 is (n + 2).

The least common multiple will be the product (n + 2)(n + 3)(n + 1). The answer choices may leave the expressions as factors, or may multiply the factors:
n³ + 6n² + 11n + 6
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Could you explain the solution a little better. I'm confused
because I thought the GCF was n² + 2, would you
mind explaining. Thanks.


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 Post subject: Re: a practice question: finding GCF and LCM (with a variabl
PostPosted: Wed Apr 04, 2012 2:22 am 
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