Final answer:
The smallest 4-digit number divisible by 2, 3, 5, and 7 is 210.
Step-by-step explanation:
To find the smallest 4-digit number divisible by 2, 3, 5, and 7, we need to find the least common multiple (LCM) of these numbers.
We can start by listing the multiples of each number:
The multiples of 2 are: 2, 4, 6, 8, 10, ...
The multiples of 3 are: 3, 6, 9, 12, 15, ...
The multiples of 5 are: 5, 10, 15, 20, 25, ...
The multiples of 7 are: 7, 14, 21, 28, 35, ...
From this list, we can find the smallest number that appears in all four lists. In this case, it is 2 x 3 x 5 x 7 = 210. Therefore, the smallest 4-digit number divisible by 2, 3, 5, and 7 is 210.