find the lcm of x^2 - 10x + 24 , x^2-8x+12 and x^2 - 6x + 8
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Factorise all the polynomials
3x
2
−6x=3x(x−2)
x
2
−4x+4=(x−2)(x−2)
x
2
+x−6=(x−2)(x+3)
The least common multiple for the first two polynomials is 3x(x−2)
2
The LCM of three polynomials is LCM of 3x(x−2)
2
and (x−2)(x−3)
⇒LCM=3x(x−2
2
)(x+3)
The highest common factor of first two polynomials is (x−2)
The HCF of all the three polynomials is HCF of (x−2) and (x−2)(x−3)
⇒HCF=(x−2)
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