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Two numbers have LCM equal to 20 times their HCF, and (LCM + HCF) = 2520. If one number is 480, what is three times (the triple of) the other number?

Difficulty: Easy

Correct Answer: 1800

Explanation:


Introduction / Context:
This is a structured HCF–LCM question with an additional sum constraint. Once HCF is determined, the product HCF * LCM gives the product of the two numbers, enabling computation of the unknown. Finally, the question asks for the triple of the other number, a simple scaling step at the end.


Given Data / Assumptions:

  • LCM = 20 * HCF.
  • LCM + HCF = 2520.
  • One number = 480.
  • Find 3 * (the other number).


Concept / Approach:
Let HCF = h, then LCM = 20h and h + 20h = 2520 ⇒ 21h = 2520 ⇒ h = 120. Product of the numbers mn = h * LCM = 120 * 2400 = 288000. Hence the other number is 288000 / 480. Multiply the result by 3 to produce the required triple.


Step-by-Step Solution:

h = 2520 / 21 = 120.LCM = 20h = 2400.mn = 120 * 2400 = 288000.Other number = 288000 / 480 = 600.Triple of the other number = 3 * 600 = 1800.


Verification / Alternative check:

Check HCF(480, 600) = 120 and LCM = (480*600)/120 = 2400. Sum = 120 + 2400 = 2520 and LCM = 20 * HCF, all consistent.


Why Other Options Are Wrong:

  • 1200, 1500, 2100 do not match the computed triple 1800 obtained from the identities and arithmetic.


Common Pitfalls:

  • Miscalculating the product mn or the final multiplication by 3.


Final Answer:

1800
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