What is the least common multiple of 3, 2 and 15?

To find the least common multiple (LCM) of 3, 2, and 15, we need to determine the smallest multiple that is divisible by all three numbers.

Let's find the prime factorization of each number:

3 is a prime number.
2 is a prime number.
15 can be factorized as 3 × 5.
Now, we identify the highest power of each prime factor that appears in any of the numbers:

The prime factor 3 appears in 3 and 15, so the highest power is 1.
The prime factor 2 appears in 2, so the highest power is 1.
The prime factor 5 appears in 15, so the highest power is 1.
To find the LCM, we multiply these prime factors with their highest powers:
LCM = 3 × 2 × 5 = 30

Therefore, the least common multiple of 3, 2, and 15 is 30.