# What is the LCM of 45 and 99?

To find the LCM of 45 and 99, we need the least number which is exactly divisible by both 45 and 99 without leaving any remainder.

## Answer: LCM of 45 and 99 is 495

The Least Common Multiple (LCM) of two numbers a and b is the smallest number which is divisible by a and b exactly.

## Explanation:

We will use two methods to find the least common multiple of 45 and 99.

- LCM of 45 and 99 by Listing Multiples Method
- LCM of 45 and 99 by Formula

### Method 1: LCM of 45 and 99 by Listing Multiples Method

We will list the first few multiples of 45 and 99 and determine the common multiples.

The least among the common multiples is the LCM of 45 and 99.

So, the LCM of 45 and 99 is 495.

### Method 2: LCM of 45 and 99 by Formula

The formula of LCM is

LCM (a,b) = (a × b) / GCF (a,b)

The Greatest Common Factor (GCF) of (45, 99) is 9. So, GCF (45, 99) = 9

So, the LCM of 45 and 99 by using the formula,

LCM (45, 99) = (45 × 99) / 9

= 45 × 11

= 495

LCM of 45 and 99 = 495

Observe that the solution to our question LCM of 45 and 99 is the same in both methods.