What is the least common multiple of 16, 19 and 8?

To find the least common multiple (LCM) of 16, 19, and 8, follow these steps:

Step 1: List the prime factors of each number.

• The prime factors of 16 are 2 x 2 x 2 x 2.
• The prime factors of 19 are 19 (since 19 is a prime number).
• The prime factors of 8 are 2 x 2 x 2.

Step 2: For each prime number, count the maximum number of times it appears in any of the prime factorizations.

• The prime number 2 appears four times in the prime factorization of 16, which is the maximum number of times it appears in any of the prime factorizations.
• The prime number 19 appears once in the prime factorization of 19, which is the maximum number of times it appears in any of the prime factorizations.

Step 3: Multiply these maximum counts of prime numbers together to get the LCM.

• The LCM is 2 x 2 x 2 x 2 x 19 = 304.

So, the least common multiple of 16, 19, and 8 is 304.