The first number can be divisible by 3 and 5 at the same time, but divisible by 7, which is 1, that is,15;

The second number is divisible by 3 and 7 at the same time, but divided by 5, it is 1, which is 21;

The third number can be divisible by 5 and 7 at the same time, but divisible by 3, that is 1, that is, 70;

Then multiply these three numbers by the remainder divided by 7, 5 and 3 respectively and add them, that is,15× 2+21× 3+70× 2 = 233.

Finally, subtract several times of the least common multiple of 3, 5 and 7, that is, 233- 105× 2 = 23.

Answer: There are at least 23 objects, namely 105k+23 objects (k is a positive integer).