What is the smallest 6 digit number divisible by?

The question, "What is the smallest 6 digit number divisible by?" is incomplete. It doesn't specify which numbers the 6-digit number should be divisible by. Based on the provided reference, we can determine the smallest six-digit number divisible by 4, 8, 12, and 16. Let's analyze this.

According to the reference, the question should be interpreted as: what is the smallest six-digit number divisible by 4, 8, 12 and 16?

Here's the breakdown:

• The smallest six-digit number is 100,000.
• To find a number divisible by 4, 8, 12, and 16, we need to find the Least Common Multiple (LCM) of these numbers.

Calculating the LCM

1. Prime Factorization: We find the prime factors of each number:

   • 4 = 2 x 2 = 2²
   • 8 = 2 x 2 x 2 = 2³
   • 12 = 2 x 2 x 3 = 2² x 3
   • 16 = 2 x 2 x 2 x 2 = 2⁴

2. LCM Calculation: The LCM is found by taking the highest power of each prime factor present:

   • The highest power of 2 is 2⁴ = 16.
   • The highest power of 3 is 3¹ = 3.
   • Therefore, the LCM of 4, 8, 12, and 16 is 16 x 3 = 48.

3. Finding the Smallest 6-Digit Multiple: Now, we need to find the smallest 6-digit number that is a multiple of 48.

   • We start with the smallest six-digit number, which is 100,000.
   • We divide 100,000 by 48: 100000 / 48 ≈ 2083.33.
   • Since we need a whole number, we round up to the next whole number which is 2084.
   • Then multiply that by 48 : 2084 * 48 = 100032.

Therefore, the smallest 6 digit number divisible by 4, 8, 12 and 16 is 100,032.