Notes on Factorisation, HCF and LCM | Grade 7 > Compulsory Maths > Factorisation, H.C.F. and L.C.M. | KULLABS.COM

Factorisation, HCF and LCM

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Highest Common Factor(HCF)

source: www.cbsetuts.com Fig: Highest Comman Factor
source: www.cbsetuts.com
Fig: Highest Common Factor

HCF is the highest number that is the greatest thing for simplifying fractions. For example, the factors common to 12 and 3 are 2,3.

\(\therefore\) HCF of 12 and 8 is 3.

  1. HCF of monomial expressions
    We can find the HCF of the given monomial expressions just by taking the common variable with the least power. The HCF of the numerical coefficient is obtained as like in the case of arithmetic. For example,
    Find the HCF of x4y2 and x2y4
    1st expression = x4y2
    2nd expression = x2y4
    \(\therefore\) HCF = x2y2
  2. HCF of polynomial Expression
    We can find the HCF of polynomials by factorizing them. For example,
    Find HCF of ax - bx and a2 - b2
    1st expression = ax - bx= x(a-b)
    2nd expression = a2 - b2 = (a-b)(a+b)
    \(\therefore\) = (a-b)

Lowest Common Multiple (LCM)

source: www.cbsetuts.com Fig: Lowest Common Multiple
source: www.cbsetuts.com
Fig: Lowest Common Multiple

The smallest positive number that the multiple of two or more numbers is LCM. For example, the LCM of a2 and a3 is a3.

  1. Lowest common factor of monomial expressions
    We can find the LCM of the given monomial expressions just by taking the common variable with the highest power. For examples,
    1sr expression = ax2
    2nd expression = a2x2
    \(\therefore\) a2x2
  2. LCM of polynomial expressions
    To find LCM of polynomial expressions . We should factorize them. Then the product of a common factors and remaining factors is the LCM of the given expressions. For examples,
    Find the L.C.M of ax2 + ax and a2x2 + a2x
    1st expression = ax2 + ax = ax(x+1)
    2nd expression = a2x2 + a2x = a2x(x+1)
    \(\therefore\) LCM = a2x(x+1)



  • We can find the HCF of the given monomial expressions just by taking the common variable with the least power.
  • We can find the HCF of polynomials by factorizing them.
  • We can find the LCM of the given monomial expressions just by taking the common variable with the highest power. 
  • To find LCM of polynomial expressions . We should factorize them. Then the product of a common factors and remaining factors is the LCM of the given expressions. 
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Questions and Answers

Click on the questions below to reveal the answers

Solution:

1st expression = x4y2

2nd expression = x2y4

\(\therefore\) HCF = x2y2

Solution:

1st expression = 4ab2

 = 2×2ab2

2nd expression = 6a2b3

 = 2×3a2b3

\(\therefore\) HCF = 2ab2

Solution:

1st expression = ax - bx = x(a-b)

2nd expression = a2 -b2 = (a+b)(a-b)

\(\therefore\) HCF = (a-b)

Solution:

1st expression = x2 + xy + zx + yz = x(x+y) + z(x+y) = (x+y) (x+z)

2nd expression = x2 - y2 = (x+y) (x-y)

\(\therefore\) HCF = (x+y)

Solution:

1st expression = 4x3y3

 = 2×2x3y3

2nd expression = 6xy

 = 2×3xy

\(\therefore\) LCM = 2×2×3 x3y3

 = 12x3y3

Solution:

1st expression = ax2 + ax = ax(x+1)

2nd expression = a2x2 + a2x = a2x(x+1)

\(\therefore\) LCM = a2x(x+1)

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  • What is the H.C.F. of x4yand x2y4

    xy4
    x2y2
    x4y
    x4y4
  • What is the H.C.F. of 4ab2 and 6a2b3

    2a3b
    2ab
    2ab2
    2a2b2
  • Find the L.C.M. of ax2 and a2x2

    ax2
    ax
    a2x
    a2x2
  • Find the L.C.M. of 4x3y3 and 6xy

    x3y3
    24x3y3
    12x3y3
    6xy3
  • Find the L.C.M. of a2 + a and a2 - 1

    a + 1
    a - 1
    a+ 1
    a(a2 - 1)
  • Find the H.C.F of ax - bx and a2 - b2

     a - b
    a+ b2 + x
    x(a - b)2
    x(a + b)
  • Find the H.C.F. of p4q3 and p3q4

    pq
    p4q4
    p2q2
    p3q3
  • Find the L.C.M. of a2 and a3

    a5
    a2
    a6
    a3
  • Find the L.C.M. of 2x + 4 and x2 + 2x

    (x - 2)2
    2x(x + 2)
    (x + 2)2
    2(x - 2)
  • Find the H.C.F. of x3 - x2y and x2 - y2

    x2 - y2
    x - y 
    x3 + y3
     x + y 
  • Find the L.C.M. of a2 - 5a + 3ab - 15ab and ax - 5x

    3x(a - b)
    x(a - 5) (a + 3b)
    2x + 3x - y
    5x - a + 3b
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