The HCF of two numbers is 74 and their LCM is 12210. If one of the numbers is 1110, what is the sum of the two numbers?

Mathematics ·Previously asked in JKSSB Wildlife Guard 2026

View the full solved paper: Wildlife Guard 8 March 2026

Question

The HCF of two numbers is 74 and their LCM is 12210. If one of the numbers is 1110, what is the sum of the two numbers?

  1. A. 1268
  2. B. 1924 (Correct answer)
  3. C. 1944
  4. D. 1428

Correct Answer

Option B — 1924

Detailed Solution & Explanation

The correct answer is 1924.

Key Points

  • This is solved using the fundamental relationship between two numbers, their HCF and their LCM:
  • Product of two numbers = HCF × LCM.
  • Given HCF = 74, LCM = 12210, and one number = 1110.
  • Let the other number be N.
  • 1110 × N = 74 × 12210 = 903540.
  • So N = 903540 ÷ 1110 = 814.
  • The sum of the two numbers = 1110 + 814 = 1924.
  • Verification: HCF(1110, 814) = 74 ✓ (1110 = 74 × 15, 814 = 74 × 11).
  • the identity HCF × LCM = product of the numbers holds for exactly two numbers (not three or more).
  • It lets you find a missing number, HCF or LCM whenever the other three are known.

Exam Tip

  • always compute HCF × LCM first, then divide by the known number — this avoids factorising the large LCM.

Topics covered: HCF & LCM