Question

If two positive integers a and b are written as a = x³y² and b = xy³, where x, y are prime numbers, then the result obtained by dividing the product of the positive integers by the LCM (a, b) is ______.

Options

• xy

• xy²

• x³y³

• x²y²

Answer 1

If two positive integers a and b are written as a = x³y² and b = xy³, where x, y are prime numbers, then the result obtained by dividing the product of the positive integers by the LCM (a, b) is xy².

Explanation:

Given, 

a = x³y²

b = xy³

∴ a × b = x³y² × xy³

= x⁴y⁵

a = x³y² = x × x × x × y × y

b = xy³ = x × y × y × y

LCM = x³y³

Product ÷ LCM

`(x^4y^5)/(x^3y^3)` = xy²