# LCM and HCF Shortcut Tricks and Formulas

**LCM and HCF Shortcut Tricks - Page 2**

** LCM and HCF Important Questions - Page 3**

** LCM and HCF Video Lecture - Page 4**

## Least Common Multiple (LCM) & Highest Common Factor(H.C.F)

Least Common Multiple (LCM) of two or more numbers is the smallest number that is a multiple of all the numbers.

LCM of 3 and 4 = 12 because 12 is the smallest multiple which is common to 3 and 4 (In other words, 12 is the smallest number which is divisible by both 3 and 4)Example:

## LCM Example and Shortcuts

**How to find out LCM using prime factorization method**

We can find LCM using prime factorization method in the following steps

Step1 : Express each number as a product of prime factors.

Step2 : LCM = The product of highest powers of all prime factors

* Example 1 : Find out LCM of 8 and 14* Express each number as a product of prime factors. (Reference: Prime Factorization and how to find out Prime Factorization)

Step1 :

14 = 2 χ 7

* Step2 : *LCM = The product of highest powers of all prime factors

Here the prime factors are 2 and 7

The highest power of 2 here =

The highest power of 7 here = 7

Hence LCM = χ 7

**Example 2 : Find out LCM of 18, 24, 9, 36 and 90**

* Step1 : *Express each number as a product of prime factors (Reference: Prime Factorization and how to find out Prime Factorization).

18 = 2 χ

24 = χ 3

9 =

36 = χ

90 = 2 χ 5 χ

* Step2 : *LCM = The product of highest powers of all prime factors

Here the prime factors are 2, 3 and 5

The highest power of 2 here =

The highest power of 3 here =

The highest power of 5 here = 5

Hence LCM = χ χ 5 = 360

Hence Least common multiple (L.C.M) of 18, 24, 9, 36 and 90 = 2 × 2 × 3 × 3 × 2 × 5 = 360

**How to find out LCM using Division Method (shortcut )**

* Step 1 :* Write the given numbers in a horizontal line separated by commas.

*Divide the given numbers by the smallest prime number which can exactly divide at least two of the given numbers.*

**Step 2 :***Write the quotients and undivided numbers in a line below the first.*

**Step 3 :***Repeat the process until we reach a stage where no prime factor is common to any two numbers in the row.*

**Step 4 :***LCM = The product of all the divisors and the numbers in the last line.*

**Step 5 :****Example 1 :** Find out LCM of 8 and 14

**Example 2 :** Find out LCM of 18, 24, 9, 36 and 90

Hence Least common multiple (L.C.M) of 8 and 14 = 2 × 4 × 7 = 56