A) prime
B) co-prime
C) composite
D) equal
Correct Answer: D
Solution :
| Sol. [d] Let the two numbers be a and b. |
| Given, \[HCF(a,b)=LCM(a,b)=k(say)\] |
| Since, \[HCF(a,b)=k\Rightarrow a=km\]and \[b=kn,\] for some natural numbers m, n. |
| We know, \[HCF\times LCM=\]Product of two numbers |
| \[\therefore \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,k\times k=km\times kn\] |
| \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,1=m\cdot n\] |
| \[\Rightarrow \,\,\,\,\,\,\,\,\,m=n=1,\]since, m, n are natural numbers. |
| Therefore, \[a=km=k\] and \[b=kn=k\] |
| \[\Rightarrow \,\,\,\,a=b=k\]i.e., the numbers must be equal. |
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