Question

Write a seven digit number without repeating any digit which is divisible by $2,3,4,6,8,9,11$

Answer 1

We have to find a seven digit number with no repeated digits such that it is divisible by $2,3,4,6,8,9,11$

First find the least common multiple of the numbers $2,3,4,6,8,9,11$

$8\times 9\times 11=792$

To get the required number take any multiple of $792$ containing $7$ different digits.

This number is divisible by each of $2,3,4,6,8,9,11$ as it is the product of least common multiple of these numbers.

Two such numbers with unique digits can be found as follows:

$792\times 1304=1032768$

$792\times 5184=4105728$