What is the LCM of (8x³ + 80x² + 200x) and (4x⁴ + 16x³ - 20x²)?

Question

Question

This question was previously asked in

SSC CGL 2022 Tier-I Official Paper (Held On : 07 Dec 2022 Shift 1)

Answer 1

Given Equation:

(8x3 + 80x2 + 200x) and (4x4 + 16x3 - 20x2)

Concept Used:

LCM is taking the least common multiples

Calculations:

First we will take the common from the equations

⇒ 8x3 + 80x2 + 200x

⇒ 8x(x² + 10x + 25)

⇒ 8x(x2 + 5x + 5x + 25)

⇒ 8x{x(x+ 5) + 5(x + 5)}

⇒ 8x(x + 5)(x + 5)

Now we take common from the second equation

⇒ 4x4 + 16x3 - 20x2

⇒ 4x² (x² + 4x - 5)

⇒ 4x2 (x2 - x + 5x - 5)

⇒ 4x2 {x(x - 1) + 5(x - 1)}

⇒ 4x2 (x - 1)(x+ 5)

Now we have to take common from the two equations

⇒ 1st equation = 8x(x + 5)(x + 5)

⇒ 2nd equation = 4x2 (x - 1)(x+ 5)

⇒ LCM = 8x2(x + 5)2(x - 1)

⇒ Hence, Option 1 is correct