To be divisible by each of the integers below 23 save for 19, it is necessary and sufficient to be divisible by each integer below 19, as 20 is covered by 5 and 4, 21 is covered by 3 and 7 and 22 by 2 and 11.

The LCM of the first 18 whole numbers is 12,252,240 (2^4 * 3^2 * 5 * 7 * 11 * 13 * 17) so we need only check multiples of that number and find any that are 10-digit pandigital.  There are four of them:

2438195760

3785942160

4753869120

4876391520

from the program where we check all 10-digit multiples for being pandigital, and stop the search as soon as 10 digits are exceeded.

DefDbl A-Z

Dim crlf$

Private Sub Form_Load()

 Form1.Visible = True

 

 

 Text1.Text = ""

 crlf = Chr$(13) + Chr$(10)

 

 unit = 12252240

 n = 10 * unit

 Do

   n = n + unit

   ns$ = LTrim(Str(n))

   If Len(ns) = 10 Then

   good = 1

   For i = 1 To 10

     If InStr(ns, Mid("0123456789", i, 1)) = 0 Then good = 0: Exit For

   Next

   If good Then

     Text1.Text = Text1.Text & n & crlf

   End If

   End If

   DoEvents

 Loop Until Len(ns) > 10

 

 

 

 Text1.Text = Text1.Text & crlf & " done"

  

End Sub