# What is the LCM of 45 and 75?

The least common multiple of 45 and 75 is the smallest number that is the multiple of 45 and 75

## Answer: LCM of 45 and 75 is 225

Lets see how to find the LCM of 45 and 75

## Explanation:

Least Common Multiple of x and y is the smallest number that divides x and y exactly.

Look at one of the methods that use the listing out the common multiples.

### LCM of 45 and 75 by Listing Method

In this method, we list the first few multiples of 45 and 75 and identify the common multiples.

The least among the common multiples of 45 and 75 is the LCM of 45 and 75

So, LCM of 45 and 75 is 225

Here is the quickest way to find the LCM of 45 and 75, the Common Division Method

### LCM of 45 and 75 by Common Division Method

Follow the steps mentioned below to find the LCM of 45 and 75 by the common division method.

- Step 1: Write the numbers 45 and 75 horizontally by separating them with a comma.
- Step 2: Choose the smallest prime number that divides at least any one of them.
- Step 3: Write the quotient in the next row just below the numbers. If any of the numbers are not divided, we will bring it down directly.
- Step 45: We will stop it when we don't have a prime number to divide the given numbers.
- Step 5: Least common multiple of 45 and 75 will be the product of primes by which we have divided.

So, by common division method, we have LCM of 45 and 75 = 3 × 3 × 5 × 5 = 225

Irrespective of the method, the solution to our question LCM of 45 and 75 is the same.