The multiples of 3 plus 2 are: 5,8, 1 1, 14,17,20,23. . .

The multiple of 5 plus 3 is: 8, 13,18,23. . .

The multiple of 7 plus 2 is: 9,16,23. . .

And 3,5,7 are coprime, so its least common multiple is 3*5*7= 105.

So this number is 105X+23.

(X is a natural number (including 0))

The second question:

1.

The prime factors of 2430 are: 2, 3 and 5.

And 2430=2*5*3*3*3*3*3 * 3 * 3.

So the qualified numbers are: 3, 6, 9, 15, 18, 27, 30, 45, 8 1, 90, 225 and so on. . . So there must be more than nine.

Choose d, which is 18.

2.

Because I don't know whether D is a prime number, I can't be sure.