**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 numerators*HCF of denominators

HCF of fractions = *HCF of numerators*LCM 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.

I Hope, this article will help you lot to understand the properties of LCM & HCF, & in solving various problems related to this article, if you still have any doubts related to this article, you can ask it into the comment section. If you have any problem in any topic mathematics you can post your problem in the comment section. You will get a reply shortly.