Graduate Management Admission Test (GMAT) Practice Test

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If two integers have no factors in common, what are their GCF and LCM?

GCF = 0, LCM = sum of the integers
GCF = 1, LCM = product of the integers
GCF = product of the integers, LCM = 1
GCF = 1, LCM = sum of the integers

The correct answer is: GCF = 1, LCM = product of the integers

When two integers have no factors in common, this means that they are coprime or relatively prime. The concept of greatest common factor (GCF) and least common multiple (LCM) for such integers can be defined clearly. For integers that are coprime, their greatest common factor is 1. This is because the only positive divisor that both numbers share is 1. Hence, the GCF is indeed 1. On the other hand, the least common multiple (LCM) of two integers can be determined using the relationship between GCF and LCM. Specifically, for any two integers, the product of the two integers equals the product of their GCF and LCM. Therefore, if the GCF is 1, then the LCM can simply be calculated as the product of the two integers. To summarize: for any two coprime integers, they have a GCF of 1 and their LCM is the product of those integers. This makes it clear why the correct choice states that the GCF is 1 and the LCM is the product of the integers.