If the sum of LCM and HCF of two numbers is 1260 and their LCM is 900 more than their HCF, then the product of two numbers is

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203400

194400

198400

205400

answer is B.

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Detailed Solution

Given,the sum of LCM and HCF of two numbers is 1260 and LCM is 900 more than their HCF.
Let a and b be two numbers and let x be the LCM and y be the HCF.
Sum of LCM and HCF of two numbers is 1260.

⇒ x + y = 1260 … … (1) LCM is 900 more than their HCF ⇒ x − y = 900 … … (2)

Add (1) and (2)

x + y + x − y = 1260 + 900 ⇒ 2 x = 2160 ⇒ x = 21602 ⇒ x = 1080 That is, LCM (a, b) = 1080

Subtract (2) from (1)

x + y − (x − y) = 1260 − 900 ⇒ 2 y = 360 ⇒ y = 3602 ⇒ y = 180

That is, HCF (a, b) = 180.

a × b = L C M (a, b) × H C F (a, b) = 1080 × 180 = 194400

Therefore, product of two numbers is 194400.
Hence the correct option is 2.

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