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 November 30th, 2015, 07:47 AM #1 Senior Member     Joined: Oct 2013 From: Far far away Posts: 429 Thanks: 18 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.
 November 30th, 2015, 02:08 PM #2 Math Team   Joined: Nov 2014 From: Australia Posts: 689 Thanks: 244 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. Thanks from shunya

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