# 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 divides 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