Question

The gcf of two numbers less than or equal to 12 is 2. Their LCM is 20.What are the numbers?

Answer 1

We know:

$LCM(a,\ b)=\dfrac{ab}{GCF(a,\ b)}$

We have

$GCF(a,\ b)=2,\ LCM(a,\ b)=20,\ a\leq12,\ b\leq12$

Substitute:

$20=\dfrac{ab}{2}\qquad|\cdot2\\\\ab=40$

$40=1\cdot40=2\cdot20=4\cdot10=5\cdot8$

Only 4 and 10 meet the requirements of the question.

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40 and 1 NOT, because 40 > 12

20 and 2 NOT, because 20 > 12

5 and 8 NOT because GCF(5, 8) = 1