# Python Program for Smallest K digit number divisible by X

• Difficulty Level : Medium
• Last Updated : 22 Jun, 2022

Integers X and K are given. The task is to find smallest K-digit number divisible by X. Examples:

```Input : X = 83, K = 5
Output : 10043
10040 is the smallest 5 digit
number that is multiple of 83.

Input : X = 5, K = 2
Output : 10```

An efficient solution would be :

```Compute MIN : smallest K-digit number (1000...K-times)
If, MIN % X is 0, ans = MIN
else, ans = (MIN + X) - ((MIN + X) % X))
This is because there will be a number in
range [MIN...MIN+X] divisible by X.```

## Python3

 `# Python code to find smallest K-digit ``# number divisible by X` `def` `answer(X, K):``    ` `    ``# Computing MAX``    ``MIN` `=` `pow``(``10``, K``-``1``)``    ` `    ``if``(``MIN``%``X ``=``=` `0``):``        ``return` `(``MIN``)``    ` `    ``else``:``        ``return` `((``MIN` `+` `X) ``-` `((``MIN` `+` `X) ``%` `X))``    `  `X ``=` `83``;``K ``=` `5``;` `print``(answer(X, K));` `# Code contributed by Mohit Gupta_OMG <(0_o)>`

Output :

`10043`

Time Complexity: O(logk)

Auxiliary Space: O(1)

Please refer complete article on Smallest K digit number divisible by X for more details!

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