What is the least common multiple of 4, 12, 17 and 16?

To find the least common multiple (LCM) of 4, 12, 17, and 16, we need to follow these steps:

1. First, find the prime factors of each number.

   • The prime factors of 4 are 2*2.
   • The prime factors of 12 are 223.
   • The prime factors of 17 are 17 (since 17 is a prime number).
   • The prime factors of 16 are 222*2.

2. Next, for each prime number, count the maximum number of times it appears in any of the factorizations.

   • The prime number 2 appears 4 times in the factorization of 16, which is the maximum.
   • The prime number 3 appears 1 time in the factorization of 12, which is the maximum.
   • The prime number 17 appears 1 time in the factorization of 17, which is the maximum.

3. Multiply these maximum counts of prime factors together to get the LCM.

   • So, the LCM of 4, 12, 17, and 16 is 22223*17 = 816.

Therefore, the least common multiple of 4, 12, 17, and 16 is 816.