Question

Find the HCF and LCM of $(x-1){(x-2)}^2{(x+4)}^3$ and $(x+1)(x-2){(x+4)}^4$

• A. HCF: $(x-2)$ ${(x+4)}^3$
• B. LCM: ${(x-2)}^2(x-1)(x+1){(x+4)}^4$
• C. LCM: $(x-2)$ ${(x+4)}^3$
• D. HCF: ${(x-2)}^2(x-1)(x+1)(x+4)$

Answer 1

Answer: (A), (B)

LCM: ${(x-2)}^2(x-1)(x+1){(x+4)}^4$
HCF: $(x-2)$ ${(x+4)}^3$

Clearly the common factors of the expressions
$(x-1){(x-2)}^2{(x+4)}^3$ and $(x+1)(x-2){(x+4)}^4$ are $(x-2)$ and ${(x+4)}^3$
$\therefore$ HCF = $(x-2)$ ${(x+4)}^3$ and
LCM = ${(x-2)}^2(x-1)(x+1){(x+4)}^4$