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LCM and HCF Questions Answers

Q11 :

HCF of two quadratic expressions is (x+2)(x + 2) and their LCM is x3+2x2−x−2x^3 + 2x^2 - x - 2 . The two expressions are:

A
  

x2−3x+2,x2−x−2x^2 - 3x + 2, x^2 - x -2

B
  

x2+3x+2,x2+x−2x^2 + 3x + 2, x^2 + x -2

C
  

x2+3x+2,x2−x−2x^2 + 3x + 2, x^2 - x -2

D
  

x2−3x+2,x2+x−2x^2 - 3x + 2, x^2 + x -2

View Answer
Correct Answer: B

x2+3x+2,x2+x−2x^2 + 3x + 2, x^2 + x -2

Description:

Given HCF =(x+2) LCM =x3+2x2−x−2 =(x+2)(x−1)(x+1)  Now p(x)q(x)= HCF and LCM ∴p(x)=(x+2)(x−1)=x2+x−2 ∴q(x)=(x+2)(x+1)=x2+3x+2begin{aligned} text{Given HCF } &= (x + 2) text{LCM } &= x^3 + 2x^2 - x - 2 &= (x + 2)(x - 1)(x + 1) text{ Now } p(x) q(x) &= text{ HCF and LCM} therefore p(x) &= (x + 2)(x - 1) = x^2 + x - 2 therefore q(x ) &= (x + 2) (x + 1) = x^2 + 3x + 2 end{aligned}

Q12 :

If H.C.F. of two numbers is 8, then which one of the following numbers cannot be L.C.M. of those numbers?

A
  

24

B
  

48

C
  

56

D
  

60

View Answer
Correct Answer: D

60

Description:

∵because 8 is not a factor of 60.∴therefore

∴therefore 60 cannot be LCM of these numbers.

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