HCF And LCM Formulas, Problems with Solutions

List of HCF and LCM Properties

  • Property 1

The product of LCM and HCF of any two given natural numbers is equivalent to the product of the given numbers.

LCM × HCF = Product of the Numbers

Suppose A and B are two numbers, then.

LCM{\rm{ }}\left( {A{\rm{ }}\& {\rm{ }}B} \right){\rm{ }} \times \;HCF{\rm{ }}\left( {A{\rm{ }}\& {\rm{ }}B} \right){\rm{ }} = {\rm{ }}A{\rm{ }} \times \;B

  • Property 2

HCF of co-prime numbers is 1. Therefore, LCM of given co-prime numbers is equal to the product of the numbers.

LCM of Co-prime Numbers = Product of The Numbers

  • Property 3

H.C.F. and L.C.M. of Fractions:

LCM of fractions =  = \dfrac{{{\rm{LCM \ of \ numerators}}}}{{{\rm{HCF \ of \ denominators}}}}

HCF of fractions =  = \dfrac{{{\rm{HCF \ of \ numerators}}}}{{{\rm{LCM \ of \ denominators}}}}

  • Property 4

HCF of any two or more numbers is never greater than any of the given numbers.

Example: HCF of 4 and 8 is 4

Here, one number is 4 itself and another number 8 is greater than HCF (4, 8), i.e.,4.

  • Property 5

LCM of any two or more numbers is never smaller than any of the given numbers.

Example: LCM of 4 and 8 is 8 which is not smaller to any of them.

Scroll to Top