H.C.F and L.C.M

Highest Common Factor (HCF)

The highest common factor (HCF) of the algebraic expression is the largest number that divides evenly into both numbers. It can be said as largest of all common factors.

For example, HCF of 6x³y² and 10x⁵y⁴ is 2x³y² since

HCF of 6 and 10 is 2

HCF of x³ and x⁵ is x³

and HCF of y² and y⁴ is y²

To find the HCF of compound expressions, first of all, resolve each expression into factors and then find HCF.

Example:

Find the HCF of 3x²- 6x and x²+ x - 6

Solution:

1st expression = 3x²- 6x

= 3x(x - 2)

2nd expression = x²+ x - 6

= x²+ 3x - 2x - 6

= x(x + 3) - 2(x + 3)

= (x + 3)(x - 2)

∴ = x - 2

Lowest Common Multiple (LCM)

The lowest common multiple(LCM) is found by multiplying all the factors which appear on either list. LCM of any number is the smallest whole number which is multiple of both.

For example, LCM of 6x³y² and 10x⁵y⁴ is 30 x⁵y⁴ since

LCM of 6 and 10 is 30, LCM of x³ and x⁵ and LCM of y² and y⁴ is y⁴.

To find the LCM of compound expressions, proceed as in the case of HCF and then find LCM.

Example

Find the LCM of 3x²- 6x

1^st expression = 3x²- 6x

= 3x(x - 2)

2^nd expression = x²+ x - 6

= x²+ 3x - 2x - 6

= x(x + 3) - 2(x + 3)

= (x + 3)(x - 2)

LCM = 3x(x - 2)(x + 3)