What are the least common multiple of 7, 14 and 21?

The least common multiple (LCM) of a set of numbers is the smallest multiple that is evenly divisible by all the numbers in the set. In this case, the numbers are 7, 14, and 21.

Let's break down the prime factors of each number:

7 = 7^1
14 = 2^1 * 7^1
21 = 3^1 * 7^1
To find the LCM, you need to take the highest power of each prime factor that appears in any of the numbers:

The highest power of 2 is 2^1.
The highest power of 3 is 3^1.
The highest power of 7 is 7^1.
Now multiply these highest powers together:

LCM = 2^1 * 3^1 * 7^1 = 2 * 3 * 7 = 42

So, the least common multiple of 7, 14, and 21 is 42.