The HCF and LCM of two numbers are 21 and 4641 respectively. If one of the numbers lies in between 200 and 300, then the two numbers are:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 273, 357
Both numbers are multiples of their HCF, so they can be written as 21x and 21y with x and y having no common factor. Their LCM is then 21xy:
\(21xy=4641\), so \(xy=\frac{4641}{21}=221\)
\(221=13\times17\), and 13 and 17 have no common factor, so x = 13 and y = 17
The numbers: \(21\times13=273\) (between 200 and 300) and \(21\times17=357\)