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?

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:

Verification / Alternative check:

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: