What is the least common multiple (LCM) of √2 and √3?

To compute the least common multiple (LCM) of √2 and √3, we need to understand how the LCM works with irrational numbers.

The LCM of two numbers is the smallest number that is a multiple of both. For our irrational numbers, we can express them in terms of their square roots:

• √2 = 2^1/2
• √3 = 3^1/2

The formula for the LCM in terms of the prime factors is:

• LCM(a, b) = Product of the highest powers of all prime factors in a and b

Here, ‘a’ and ‘b’ are √2 and √3, respectively. Since the numbers 2 and 3 have no common prime factors, we take:

• Max power of 2: 1/2 from √2
• Max power of 3: 1/2 from √3

So, the LCM becomes:

• LCM(√2, √3) = 2^1/2 × 3^1/2 = √(2 × 3) = √6

In conclusion, the least common multiple of √2 and √3 is √6.