Q. 5 C4.0( 4 Votes )
Let’s find the G.C.D and L.C.M. of the following expressions:
a3-4a2 + 4a, a2 + a-6, a3-8
Answer :
Factors of a3-4a2 + 4a
=a(a2-4a + 4)
=a(a-2)2
Factors of a2 + a-6
= a2 + 3a-2a-6
=a(a + 3)-2(a + 3)
=(a + 3)(a-2)
Factors of a3-8
=(a-2)(a2 + 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 a3-4a2 + 4a, a2 + a-6, a3-8 is a(a-2)2(a2 + 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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