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

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#### Highest Common Factor(HCF)

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)

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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### Very Short Questions

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)

0%

x4y4
x2y2
xy4
x4y

2ab2
2a3b
2a2b2
2ab

a2x2
ax
a2x
ax2

12x3y3
24x3y3
x3y3
6xy3

a - 1
a + 1
a+ 1
a(a2 - 1)

x(a + b)
a - b
x(a - b)2
a+ b2 + x

p3q3
pq
p2q2
p4q4

a3
a5
a2
a6

(x - 2)2
2x(x + 2)
(x + 2)2
2(x - 2)

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

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

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