Q. 5 E3.8( 5 Votes )

# 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)

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