# What is the LCM of 30 and 45?

LCM of 30 and 45 is the smallest number which is exactly divisible by all of them.

## Answer: LCM of 30 and 45 is 90

We will explain two methods to find the least common multiple of 30 and 45.

## Explanation

Least Common Multiple of 30 and 45 will be the smallest number that exactly divides 30 and 45 without leaving a remainder.

- LCM of 30 and 45 by Division Method
- LCM of 30 and 45 using Common Multiples

## Methods to Find LCM of 30 and 45

### Method 1: LCM of 30 and 45 by Division Method

In this division method, we divide 30 and 45 simultaneously with prime numbers and stop it when we don't have a prime number to divide 30 and 45 any further.

So, the least common multiple of 30 and 45 is given by 2 × 3 × 3 × 5 = 90. This means LCM(30, 45) = 90

### Method 2: LCM of 30 and 45 using Common Multiples

Multiples of 30 = 30, 60, 90, 120, 150

Multiples of 45 = 45, 90, 135, 180

Clearly, 90 is the least common factor of 30 and 45

Hence, LCM of 30 and 45 = 90