The HCF and LCM of two numbers are 7 and 140 respectively. If both numbers lie between 20 and 45, what is their sum?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 63
Two numbers with HCF 7 are \(7a\) and \(7b\), where \(a\) and \(b\) have no common factor, and their LCM is \(7ab\).
\(7ab=140\), so \(ab=20\)
Co-prime pairs with product 20: (1, 20) and (4, 5)
(1, 20) gives 7 and 140, which are not between 20 and 45
(4, 5) gives 28 and 35, both between 20 and 45
Sum \(=28+35=63\)
The sum of the numbers is 63.