The LCM of two numbers is 168 and their HCF is 12. If the difference between the numbers is 60, what is the sum of the numbers?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 108
Both numbers are multiples of the HCF, so they can be written as \(12a\) and \(12b\) with \(a\) and \(b\) co-prime. Their LCM is then \(12ab\).
\(12ab=168\), so \(ab=14\)
Co-prime pairs with product 14: (1, 14) and (2, 7)
(1, 14) gives 12 and 168, difference 156
(2, 7) gives 24 and 84, difference 60, as required
Sum \(=24+84=108\)
The sum of the numbers is 108.