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November 30th, 2015, 07:47 AM   #1
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state the conditions

Let a and b represent whole numbers. State the conditions on a and b that make the following statements true.

A) GCF(a,b) = a
My answer: A is true iff a|b

B) LCM(a,b) = a
My answer: B is true iff b|a
(A and B seem to be complementary)

C) GCF(a,b) = a * b
My answer: C is true iff a = b = 1. Otherwise C is impossible

D) LCM(a,b) = a * b
My answer: D is true iff GCF(a,b) = 1 i.e. if a and b are relatively prime.

Am I correct? Can you give me a better insight regarding this question. Thanks.
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November 30th, 2015, 02:08 PM   #2
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Does the original question say $a$ and $b$ are positive? If they're allowed to be negative, there may be some tweaking to do.
For positive integers, you are spot on.
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