# HCF & LCM: Easy Ways to Find HCF and LCM | Quantitative Aptitude

*What is HCF?*

*The highest positive integer which divides two or more integers without any remainder is called Highest Common Factor (HCF) or Greatest Common Divisor or Greatest Common Factor (GCF).*

### ♦ Factor

*A factor of a given number is every number that divi*

*des exactly into that number.*

*Steps to find HCF of Numbers:-*

*Step 1: Make prime factors of the given numbers.*

*Step 2: Take out pairs of common factors between them*

*Step 3: Multiply them to get HCF.*

**HCF Examples:**

♥ Consider the numbers 12 and 14

The Prime factors of 12 are : 2 X 2 X 3

The factors of 14 are : 2 X 7

2 is the only common factors (numbers which are factors of both 12 and 14).

Therefore, the highest common factor(HCF) of 12 and 14 is 2.

♥ Consider the numbers

24 and 28

The Prime factors of 24 are : 2 X 2 X 2 X 3

The factors of 28 are : 2 X 2 X 7

2 X 2 = 4 is the only common factors (numbers which are factors of both 24 and 28).

Therefore, the highest common factor(HCF) of 24 and 28 is 4.

*What is LCM?*

*Least common multiple (LCM) of two numbers is the smallest number (not zero) that is a multiple of both. It is also known as lowest common multiple.*

*Steps to Find LCM of Numbers:-*

*Step 1: Find the prime factorization of both numbers.*

* Step 2:Write down the most times any prime number occurs in the prime factorization of each number.*

* Step 3: Multiply all the prime factors together — multiplying each number once for each of its occurrences.*

### For Examples:

♥ Consider the numbers 12 and 14 again

The Prime factors of 24 are : 2 X 2 X 2 X 3

The factors of 28 are : 2 X 2 X 7

Since, 2 occurs maximum 2 times, 3 occurs maximum 1 time and 7 also occurs maximum 1 time

Therefore, the lowest common multiple of 12 and 14 is 2 X 2 X 3 X 7 = 84.

♥ Consider the numbers 12 and 18

The Prime factors of 12 are : 2 X 2 X 3

The factors of 18 are : 2 X 3 X 3

Since, 2 occurs maximum 2 times, 3 occurs maximum 2 time

Therefore, the lowest common multiple of 12 and 18 is 2 X 2 X 3 X 3 = 36

*Points to remember while finding HCF or LCM of Numbers*

*1. HCF X LCM = Product of two Numbers.*

* 2.HCF is always smaller than LCM.*

* 3. HCF of given numbers is not greater than any of the numbers*

* 4. LCM of given numbers is not smaller than any of the numbers.*

*watch the video to learn different ways to find HCF and LCM of Numbers*