Q. 5 D4.9( 7 Votes )

# Let’s find the G.C.D and L.C.M. of the following expressions:a2 + b2-c2 + 2ab, a2 + c2-b2 + 2ca, b2 + c2-a2 + 2bc

Answer :

factors of a2 + b2-c2 + 2ab

=(a + b)2-c2

=(a + b + c)(a + b-c)

Factors of a2 + c2-b2 + 2ca

=(a + c)2-b2

=(a + c + b)(a + c-b)

Factors of b2 + c2-a2 + 2bc

=(b + c)2-a2

=(b + c + a)(b + c-a)

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 a2 + b2-c2 + 2ab, a2 + c2-b2 + 2ca, b2 + c2-a2 + 2bc is (a + b-c)(a + c-b)(b + c-a)(a + b + c)

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

the GCD is (a + b + c)

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