Find the smallest five-digit number which always leaves a remainder of 2 when divided by 15, 30, 38, 40 respectively.

Explanation

The LCM of 15, 30, 38 and 40 is <table> <tr> <th></th> <th>2</th> <th>15,</th> <th>30,</th> <th>38,</th> <th>40</th> </tr> <tr> <td></td> <td>2</td> <td>15,</td> <td>15,</td> <td>19,</td> <td>20</td> </tr> <tr> <td></td> <td>2</td> <td>15,</td> <td>15,</td> <td>19,</td> <td>10</td> </tr> <tr> <td></td> <td>3</td> <td>15,</td> <td>15,</td> <td>19,</td> <td>5</td> </tr> <tr> <td></td> <td>5</td> <td>5,</td>