Q. 5 C4.0( 4 Votes )

# Let’s find the G.

Answer :

Factors of a^{3}-4a^{2} + 4a

=a(a^{2}-4a + 4)

=a(a-2)^{2}

Factors of a^{2} + a-6

= a^{2} + 3a-2a-6

=a(a + 3)-2(a + 3)

=(a + 3)(a-2)

Factors of a^{3}-8

=(a-2)(a^{2} + 2a + 4)

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 a^{3}-4a^{2} + 4a, a^{2} + a-6, a^{3}-8 is a(a-2)^{2}(a^{2} + 2a + 4) (a + 3)

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

∴ the GCD is (a-2)

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