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Smallest 3 digit number is 100.   We need to find that smallest number more than or equal to 100 and divisible by 4 and 6.

So it must be divisible by 12 (lcm of 4 and 6).

         100 = 8 * 12 + 4 
     In order that on the hand side, the reminder should become multiple of 12,  you must add 8 to 4.  So on the LHS, you have to add 8.

so then number is 108.