To minimize a number ending in 7 zeros, pack the smallest digits possible at the front: 1 (start), 000002 (zeros & smallest non-divisible factor). So, 1000002 is smallest.
Start with a single "1" as the first digit. This is the smallest possible non-zero digit.
Add 7 zeros to the end. So far, our number is 1000000.
Now, try adding digits to the front of the number, starting from 2 (since we already used 1).
Check if the new number is still the smallest possible:
If the new number is divisible by 2, it's not the smallest possible because we can replace the "2" with a "1" and get a smaller number with the same number of zeros.
If the new number is divisible by 3, it's not the smallest possible because we can add a "2" in front of the existing "1" and get a smaller number with the same number of zeros.
Continue adding digits and checking for divisibility by 2 and 3 until you find a number that is not divisible by either. This will be your smallest possible value of n.
Following this method, you'll find that the smallest possible value of n is 1000002.