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

x³-4x, 4(x²-5x + 6),(x²-4x + 4)

factors of x³-4x

=x(x²-4)

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

Factors of 4(x²-5x + 6)

=4(x²-3x-2x + 6)

=4{x(x-3)-2(x-3)}

=4(x-2)(x-3)

Factors of (x²-4x + 4)

=(x-2)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 x³-4x, 4(x²-5x + 6),(x²-4x + 4) is 4x(x-3)(x + 2)(x-2)²

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

∴ the GCD is (x-2)