What is the least common multiple of 28, 42, 31 and 14?

To find the least common multiple (LCM) of 28, 42, 31, and 14, follow these steps:

1. Prime factorize each number:

   • 28 = 2^2 * 7
   • 42 = 2 * 3 * 7
   • 31 = 31 (it's a prime number)
   • 14 = 2 * 7

2. For each prime number, take the highest power that appears in the factorization of each number:

   • For 2, the highest power is 2 (from 28)
   • For 3, the highest power is 1 (from 42)
   • For 7, the highest power is 1 (from 28, 42, and 14)
   • For 31, the highest power is 1 (from 31)

3. Multiply these highest powers together:

   • LCM = 2^2 * 3^1 * 7^1 * 31^1 = 4 * 3 * 7 * 31 = 2604

So, the least common multiple of 28, 42, 31, and 14 is 2604.