If f₁ = 6x²y and f₂ = 15 xy², then which of the following option is true ?

The correct answer is (D) H.C.F. (f₁, f₂) = 3xy, L.C.M. (f₁, f₂) = 30x²y².

• Factorization: $f_1 = 6x^2y = 2$$\cdot$ 3 $\cdot$ x^2 $\cdot$ y and $f_2 = 15xy^2 = 3$$\cdot$ 5 $\cdot$ x $\cdot$ y^2.
• HCF & LCM: $\text{HCF}=\gcd (6,15)\cdot x\cdot y=3xy$$\text{HCF}$ = \gcd(6, 15) $\cdot$ x $\cdot$ y = 3xy. $\text{LCM}=\text{lcm}(6,15)\cdot x^2\cdot y^2=30x^2{y}^2$$\text{LCM}$ = $\text{lcm}$(6, 15) $\cdot$ x^2 $\cdot$ y^2 = 30x^2y^2.