To find the least common multiple (LCM) of √2 and √3, we first need to understand the properties of these numbers. Since both numbers are irrational, their LCM is determined somewhat differently compared to integers.
The LCM of two numbers is the smallest number that is a multiple of both. For non-integer values, one common method is to find the LCM by using the formula:
LCM(a, b) = (a × b) / GCD(a, b)
In this case:
- Let a = √2
- Let b = √3
Since √2 and √3 are both prime numbers, their greatest common divisor (GCD) is 1. Therefore, we can simplify our calculation:
LCM(√2, √3) = (√2 × √3) / GCD(√2, √3) = (√2 × √3) / 1 = √6
Thus, the LCM of √2 and √3 is √6.