Question

find the lest 5 digit no..which on dividing by 6,9,12and 18 leaves a remaimder 3 in each case

Answer 1

The lowest common multiple of 6, 9, 12 and 18 is 36. 

So the result will be of the form 36k + 3, where k is an integer. 

You want the first number of this form that is greater than 9999 

36k + 3 > 9999 
36k > 9996 
k > 9996/36 
k > 277 2/3 

Round up to the next integer: 
k = 278 

Multiply that by 36 and add 3. 
36 * 278 + 3 
= 10011 

Double-check: 
10011 / 6 = 1668 r 3 
10011 / 9 = 1112 r 3 
10011 / 12 = 834 r 3 
10011 / 18 = 556 r 3 

Answer: 
10,011


Hope it helps