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.

Therefore, LCM of √2 and √3 does not exist