# Least Common Multiples (LCM) Formula with Examples

## What is LCM?

The smallest number which is exactly divisible by all the given Numbers that is called LCM.

There are two methods to calculate LCM of given numbers

1. Prime Factorization Method
2. Division Method

### L.C.M formula for any two numbers is,

LCM = aXb / gcd (a, b)

LCM formula for fraction is given by,

### LCM = LCM of Numerator / HCF of Denominator

For Example:

Q1. Find the LCM of (40, 45)

Solution by Method:

Given Numbers: 40, 45

Find the Greatest common Factor of given numbers

40 = 2X5X4

45 = 5X9

Gcd(40, 45)= 5

LCM= 40X45/5

LCM= 40X9

LCM=360

Solution By Method 2:

5)40, 45

1)8, 9

LCM= 5X8X9 = 360

Q2. Find the LCM of Factorial Number (5/3, 7/6, and 8/9)

Solution:

According to Formula Find LCM of Numerators 5, 7, 8

LCM = 5X7X8=280

Find HCF of Denominators 3, 6, 9 = 3

LCM = 280/3

If you not proper understand then See my YouTube Video on bases of LCM formula with Example.

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