Hcf and Lcm

HCF

What is HCF?

HCF means the largest number that divides two or more numbers exactly (without leaving any remainder).
It is also called GCD (Greatest Common Divisor).

Methods to Find HCF

1. Factor Method

Write all factors of given numbers

Find the greatest common factor

Example:

HCF of 8 and 12 = 4

2. Prime Factorization Method

Break numbers into prime factors.

Example:

18 = 2 × 3 × 3

24 = 2 × 2 × 2 × 3

Common primes → 2 × 3

 HCF = 6

3. Division Method

Divide the larger number by the smaller

Continue until remainder becomes 0

Last divisor is the HCF

Example:

HCF of 36 and 12 = 12

Important Points for Exams 

1. HCF of two prime numbers = 1
2. HCF of a number with itself = same number
3. HCF of consecutive numbers = 1
4. HCF of even and odd number = 1

Formula to Calculate HCF

 HCF × LCM = Product of the two numbers

HCF = product of the two numbers/LCM

LCM

What is LCM?

LCM means the smallest number that is exactly divisible by two or more given numbers.

Methods to Find LCM

1. Listing (Multiples) Method

Write multiples of each number

Find the smallest common multiple

Example: LCM of 3 and 5 = 15

2. Prime Factorization Method

Break numbers into prime factors.

Example:

12 = 2² × 3

18 = 2 × 3²

Take highest power of each prime

LCM = 2² × 3² = 36

3. Division Method (Fast Method)

Divide numbers by prime numbers until all become 1.

Example: LCM of 8 and 12 = 24

Important Exam Points 

1. LCM of co-prime numbers = product of the numbers
2. LCM is always greater than or equal to the largest number
3. Used in time & work, time & distance, fractions

Formula to Calculate LCM

 HCF × LCM = Product of the two numbers

LCM= product of the two numbers/HCF