Find a six digit integer Find an integer with six different digits such that the six digit integer is divisible by each of its digits.

For example, find ABCDEF such that A, B, C, D, E and F all can divide the number ABCDEF.

Show your answer along with mathematical reasoning.
The number $861432$ will work.  I guess $123864$ looks nicer.
The LCM of $1,2,3,4,5$ is $60$.

$$\frac{134520}{60} = 2242$$