# What is the LCM of root 2 and root 3?

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

## Answer: LCM of ⎷2 and ⎷3 does not exist

The Least Common Multiple (LCM) of ⎷2 and ⎷3 is the smallest number which is divisible by ⎷2 and ⎷3 exactly.

## Explanation:

We are using the listing of multiples method to find the least common multiple of ⎷2 and ⎷3

We will list the first few multiples of ⎷2 and ⎷3 and determine the common multiples.

The least among the common multiples is the LCM of ⎷2 and ⎷3

- Multiples of ⎷2: ⎷2, 2, 2⎷2, 4, 4⎷2, 8, 8⎷2, 16, 16⎷2, 32, 32⎷2...
- Multiples of ⎷3: ⎷3, 3, 3⎷3, 9, 9⎷3, 27, 27⎷3, 81,...

Since both ⎷2 and ⎷3 do not have any common multiple, so LCM of ⎷2 and ⎷3 does not exist.

Also, both numbers ⎷2 and ⎷3 are irrational numbers and the LCM of two irrational numbers does not exist.