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What is the smallest positive five-digit integer, with all different digits, that is divisible by each of its non-zero digits? (The number itself may have 0 as a digit.)

 Feb 23, 2020
 #1
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I'm getting 12384, which is divisible by 1, 2, 3, 8, and 4.

 Feb 23, 2020
 #2
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The smallest positive 5-digit integer =10236

 Feb 23, 2020
 #3
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What is the smallest positive five-digit integer, with all different digits, that is divisible by each of its non-zero digits? (The number itself may have 0 as a digit.) 

 

Does the problem allow the 5-digit integer to begin with a zero? 

 

If so, then submitted for your approval is the number 01236 

 

The problem does not explicity prohibit the leading zero. 

If you make the assumption that a leading zero is not allowed,

and I make the assumption that a leading zero is allowed, 

then who says my assumption is less valid than yours?

.

 Feb 23, 2020

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