Finding the second number — Number System Aptitude Question
Finding the second number: The HCF of two numbers is 11 and their LCM is 693. If one of the numbers is 77, what is… Answer and worked solution on CodeKairo.
- Topic: Number System
- Section: Quantitative Aptitude
- Difficulty: Easy
- Time target: 45 seconds
Question
The HCF of two numbers is 11 and their LCM is 693. If one of the numbers is 77, what is the other?
Options
- 66
- 88
- 99
- 121
Show the answer and the worked solution
Correct answer: C. 99
Worked solution
- HCF × LCM = first × second, so 11 × 693 = 77 × second.
- Second = 7623 ÷ 77 = 99.
- Check: HCF(77, 99) = 11 and LCM(77, 99) = 693. ✓
Answer: 99.
The idea
The identity HCF × LCM = a × b holds only for two numbers. Always verify the answer by checking that the HCF of the pair really is what was given.
Shortcut. The other number must divide the LCM 693 = 3² × 7 × 11. 66 and 88 are even and 121 needs 11², so only 99 fits.
Common trap. 66 — like every option it shares HCF 11 with 77, so a check of the HCF alone passes it; its LCM with 77 is 462, not 693.