**Factors and Multiples -Factors, Common Factors, Highest Common Factors (H.C.F.)**

**and**

**Multiples, Common Multiples, Lowest Common Multiples (L.C.M.)**

We know that the exact divisor of a number is called its factor. For example 10 is exactly divisible by 5 and so, we can say that 5 is the factor of 10.

** **Let us consider some numbers, say 8, 12 and 20

### Now, we have

Common Factors of 8, 12 and 20 are **1**, **2** and **4**

Highest Common Factor of 8, 12 and 20 is **4**

** ****4** is the largest number which divides 8, 12 and 20 that is, **4 **is largest exact divisor of 8,12 and 20 and so, we can say that HCF of 8,12 and 20 is **4**

** **Hence,

The largest number which divides exactly two or more numbers is called the **Highest Common Factors (H.C.F.)** of the numbers.

Or

The largest number which is the exact divisor of two or more numbers is called the **Highest Common Factors (H.C.F.)** of the numbers.

__ __Let us consider some numbers, say 4, 6 and 8

Then, we have

From above, we see that

Now, common multiples of 4, 6 and 8 are ** 24**,

**and**

__48__

__72__

Lowest Common Multiple of 4, 6 and 8 is ** 24 **and so, we can say that

**L.C.M. of 4, 6 and 8 is 24**

In other words, we can say that **24** is the smallest number which is exactly divisible by 4, 6 and 8

### Hence,

The smallest number which is exactly divisible by two or more numbers is called the Lowest Common Multiple (L.C.M.) of the numbers.

__RELATION BETWEEN TWO NUMBERS__

__RELATION BETWEEN TWO NUMBERS__

The Product of two numbers is equal to the Product of the HCF and LCM of the two numbers. This is the mathematical relation between two numbers.

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**Product of two numbers** = **Product of the HCF and LCM of two numbers**

** **

Let us understand this concept by taking two numbers, say **8 **and **12**

** **

Here, we have

HCF of 8 and 12 = 4

LCM of 8 and 12 = 24

From (i) and (ii), we get

**8** × **12** = HCF of 8 and 12 × LCM of **8** and **12**

** **

Hence, it is well established that

**Product of two numbers** = **Product of the HCF and LCM of two numbers**

**If you have any Questions, Regarding this post, Please Give Comments Below.**

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