The LCM of two numbers is 180 and their HCF is 6. If one number is 36, what is the other number?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 30
For any two numbers, HCF \(\times\) LCM \(=\) product of the numbers.
36 \(\times\) other \(=6\times180=1080\)
Other \(=1080\div36=30\)
Check: HCF of 36 and 30 is 6, LCM is 180
The other number is 30.
Why the other options are incorrect
Option (1) 18 — Incorrect. With 36 and 18 the HCF is 18 and the LCM is 36, not 6 and 180.
Option (2) 60 — Incorrect. With 36 and 60 the HCF is 12 and the LCM is 180, not 6 and 180.
Option (3) 45 — Incorrect. With 36 and 45 the HCF is 9 and the LCM is 180, not 6 and 180.