We know:
[tex]LCM(a,\ b)=\dfrac{ab}{GCF(a,\ b)}[/tex]
We have
[tex]GCF(a,\ b)=2,\ LCM(a,\ b)=20,\ a\leq12,\ b\leq12[/tex]
Substitute:
[tex]20=\dfrac{ab}{2}\qquad|\cdot2\\\\ab=40[/tex]
[tex]40=1\cdot40=2\cdot20=4\cdot10=5\cdot8[/tex]
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
The numbers are 4 and 10 or 5 and 8.
The relation is given as,
[tex]LCM*GCF=m*n[/tex]
Where m and n are two numbers.
Given that, [tex]GCF=2,LCM=20[/tex]
Substitute values in above relation.
[tex]m*n=2*20=40[/tex]
Since, both numbers less than or equal to 12.
We observed that,
[tex]4*10=40\\\\5*8=40\\[/tex]
The numbers are 4 and 10 or 5 and 8.
Learn more about greatest common factor here:
https://brainly.com/question/16054958
