The ratio of two numbers is 5 : 6 and their HCF is 8. What is the LCM of these numbers?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 240
Numbers in the ratio 5 : 6 can be written as \(5k\) and \(6k\). Since 5 and 6 have no common factor, \(k\) itself is the HCF, so \(k=8\).
The numbers: \(5\times8=40\) and \(6\times8=48\)
LCM \(=8\times5\times6=240\)
Tip: For two numbers, HCF \(\times\) LCM \(=\) product of the numbers: \(8\times240=1920=40\times48\). This gives the LCM at once when the HCF and the numbers are known.