## Properties of LCM And HCF

Before understanding the Properties of LCM And HCF, you have to understand the basic concepts & definition of HCF And LCM.

There are many properties of LCM and HCF :

### Property 1

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

LCM × HCF = Product of the Numbers

If A and B are two numbers, then.

LCM (A & B) × HCF (A & B) = A × B

### Property 2

The H.C.F. of two or more numbers can not be greater than any one of them.

For example, the H.C.F. of 16, 18 and 24 is 2 which is less than all the given numbers.

### Property 3

If one number is a factor of the other numbers, their H.C.F. will be always that smallest number.

For example, 9 is the H.C.F. of 18, 36 and 45.

Because 18, 36 and 45 is the factor of 9.

### Property 4

HCF of co-prime numbers is always 1.

HCF of Co-prime Numbers = 1

### Property 5

LCM of given co-prime numbers is equal to the product of the numbers.

LCM of Co-prime Numbers = Product Of The Numbers

### Property 6

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

LCM of fractions = LCM of numeratorsHCF of denominators

HCF of fractions = HCF of numeratorsLCM of denominators

Example: Find the HCF of 1225, 910, 1835, 2140

Solution: The required HCF is = HCF of 12,9,18,21
LCM of 25,10,35,40 = 31400

### Property 7

The L.C.M. of two or more numbers is not less than any of the given numbers.

### Property 8

LCM of given numbers is a multiple of their HCF.
For example, HCF of 16, 12 = 4
LCM of 16, 12 = 48
LCM 48 is a multiple of HCF 4.