Let’s find the G.C.D and L.C.M. of the following expressions:

x³-8, x² + 3x-10, x³ + 2x²-8x

Factors of x³-8

=(x-2)(x² + 2x + 4)

Factors of x² + 3x-10

= x² + 5x-2x-10

=x(x + 5)-2(x + 5)

=(x + 5)(x-2)

Factors of x³ + 2x²-8x

=x(x² + 2x-8)

=x(x² + 4x-2x-8)

=x{x(x + 4)-2(x + 4)}

=x(x + 4)(x-2)

LCM is the lowest common multiple, which is the product of all the common factors taken once and the remaining factors as it is.

∴ the LCM of x³-8, x² + 3x-10, x³ + 2x²-8x is x(x-2)(x² + 2x + 4) (x + 4)(x + 5)

GCD is the greatest common divisor, which is equal to the product of all the common divisors.

∴ the GCD is (x-2)