The HCF and LCM of two numbers are 33 and 4719 respectively. When the first number is divided by 3, the quotient is 121. Find the…

Question

The HCF and LCM of two numbers are 33 and 4719 respectively. When the first number is divided by 3, the quotient is 121. Find the other number.

1. A. 424
2. B. 433
3. C. 469
4. D. 429 (Correct answer)

Correct Answer

Option D — 429

Detailed Solution & Explanation

The correct answer is 429.

Key Points

• First find the unknown 'first number' from the division clue, then use the HCF × LCM = product rule.
• 'When the first number is divided by 3, the quotient is 121', so the first number = 3 × 121 = 363.
• Now apply Product of two numbers = HCF × LCM:
• 363 × (other number) = 33 × 4719 = 155727.
• So the other number = 155727 ÷ 363 = 429.
• Verification: HCF(363, 429) = 33 ✓ (363 = 33 × 11, 429 = 33 × 13) and LCM = 33 × 11 × 13 = 4719 ✓.
• the relation HCF × LCM = product of the two numbers is the single most tested identity in the HCF/LCM chapter of JKSSB, SSC and railway exams.

Exam Tip

• read the wording carefully — 'quotient is 121' means multiply back (363), a step candidates often skip.