In this article we explain LCM And HCF Definition, Formula, Relation between lcm and hcf, questions

### LCM And HCF Definition

#### LCM Definition ( Least Common Multiple )

The least common multiple of two or more numbers or expressions is the smallest number Or is an expression with a minimum of a square that is completely divisible by the given numbers or expressions.

Examples

Finding the least common multiple of 6, 8, 12 numbers.

The numbers divided by 6 are 6, 12, 18, 24, 30, 36

The numbers 8, 16, 24, 32, 40, divided by 8

The numbers 8, 16, 24, 32, 40, divided by 8

Numbers divided by 12 are 12, 24, 36

24 is the least common number among the numbers divided by these three numbers, so the least common multiple of these numbers is 24.

Similarly, the least common multiple of xЗ, x２, x５, x４ is x５.

Multiples of xЗ =, x４, x５, x６

Multiples of x２ = x２, xЗ, x４, x５, x６

Multiples of x５ = x５, x６, x７

Multiples of x４ = x４, x５, x６, x７

The common expression with the minimum address = x５. Thus, the least common multiple = x５

#### Method Of Finding LCM ( Least Common Multiple )

There are two methods to find the LCM .

#### Factor Method

In this method we first do a prime factorization of numbers.

Then we get the product of each factor of more powers.

For example, to find the least common multiple of 6,8,12, one must first do a prime factorization of these numbers.

Prime factorization of 6 = 2 × 3

Prime factorization of 12 = 2 × 2 × 3

Prime factorization of 8 = 2 × 2 × 2

Note – When we find the least common multiple, we include the common numbers as well as the other remaining numbers.

Explanation

Step 1 — The prime factor of 6,12,8 will include the common number 2. The following is the picture.

Step-2 Common will take 2 out of the prime factors of 8,12. In the following figure.

**Step-3** Common will take 3 out of the prime factors of 6,12. In the following figure.

**Step-4**Finally, the number 2 in the prime factor of 12 will also be included. In the following figure.

Thus, after following all the steps, the least common multiple of the number 6,8,12 = 2 x 2 x 3 x 2 = 24

**Example-2**

Find the least common multiple of xy, x２y, xy２?

**Solve**– The least common multiple of x 2 y = x❌x ❌y.

The least common multiple of x y2 = x❌y ❌y

The least common multiple of x y = x❌y

x y, x 2 y, the least common multiple of x y2 = x 2 y2

0000000000000

**Explanation**

**Step**-1 Common number in the factors of x y, x 2 y, x y2 = X . In the picture.

**Step-2**Common number in the factors of x y, x 2 y, x y2 =Y . In the picture.

**Step-3 **At the end, the remaining XY will be included in the factors of x 2 y, x y2.

**Step-4**

### Division Method

**Example**

### Highest Common Factor

#### Defination of Highest Common Factor

**Example**

#### Method of finding HCF

**1. Factor Method**

**Example**

**2. Division Method**