The sum of LCM and HCF of two numbers is 854. If the LCM is 60 times the HCF and one of the numbers is 70, then the other number is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 168
For any two numbers, LCM \(\times\) HCF \(=\) product of the two numbers. The LCM and HCF are found first from the two facts given; the other number is then their product divided by 70.
LCM \(=60\times\) HCF, so \(60\,\text{HCF}+\text{HCF}=854\)
\(61\,\text{HCF}=854\), so HCF \(=14\)
LCM, 60 times the HCF \(=60\times14=840\)
Other number \(\displaystyle =\frac{840\times14}{70}=168\)