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# What is the difference between HCF and LCM ?

The key to tell the difference between LCM and HCF is to know the difference between a multiple and a factor.

### What is a multiple?

A multiple of a number is any number that appears in its times table.

For example, the multiples of 3 are 3, 6, 9, 12 and so on.

### What is a factor?

A factor of a number is any integer that divides that number without leaving any remainder.

For example factors of 9 are 1, 3 and 9.

To know the difference between HCF and LCM of two numbers we must know the meaning of HCF and LCM first.

HCF

HCF is defined as the Highest Common Factor of two or more given numbers.

It is also called Greatest Common Divisor (GCD).

For example:

The HCF of 36 and 24 is 12, because 12 is the largest number that divides both the numbers completely without leaving any remainder.

LCM

LCM is the Least Common Multiple of two or more numbers. It turns out to be the smallest number that is a common multiple of the given numbers.

Example: Let us take two numbers 16 and 8

Multiples of 16 are:  16, 32, 48, 64, 80, 96 and so on.

Multiples of 8 are : 8 , 16 , 24 , 32 , 40  , 48 , 56 , 64 and so on .

We can see from above that the first common value among these multiples is 16.

Therefore, 16 is the LCM or least common multiple of the two numbers 16 and 8.

Now this was about the meaning of HCF and LCM.

From the above discussion we can conclude that LCM and HCF are two entirely different concepts with following differences:

### Differences between HCF and LCM

#### 1). Definition

The main difference between HCF and LCM lies in their definitions.

While HCF is all about calculating the highest number that divides a given number into two or more equal parts, LCM means finding a common multiple of the lowest value shared by the given numbers.

#### 2).  Full Form

HCF stands for Highest common factor for two or more given numbers. LCM is the abbreviation used for the Least Common Multiple for two or more numbers.

#### 3). Type

The LCM number is generally a composite number when calculated correctly. Whereas the HCF can either be a prime number or composite number depending on the given numbers.

While HCF is the largest real number shared by all the given numbers, LCM is the smallest number that can be divided by the given numbers.

#### 4). Other names

HCF is also as GCF or GCD while LCM is more or less the only term used to convey the least multiple which is common to a given set of numbers.

#### 5). Calculations

The methods of finding both LCM and HCF are different from each other.  Though it says “least” common multiple, the answer is always greater than the numbers.

Similarly, for HCF. It says “Highest” common factor, the answer is always lowest from all the three numbers.

For example:

Find the LCM and HCF of 10, 15 and 20.

#### For LCM, Let’s use the ladder method

 2 10, 15, 20 2 5, 15, 10 3 5, 15, 5 5 5, 5, 5 1, 1, 1

LCM of 10, 15 and 20 is 2 * 2* 3 * 5 = 60

For HCF, we need to calculate the factors and then find the common amongst them.

Factors of 10: 1, 2, 5, 10

Factors of 15: 1, 3, 5, 15

Factors of 20: 1, 2, 4, 5, 10, 20

The common factors are 1 and 5, out of which 5 is the biggest number.  This means 5 is the HCF of 10, 15 and 20.