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Python Program for Smallest K digit number divisible by X

Last Updated : 23 Jul, 2025
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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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