Question

determine the smallest 3 digit number which exactly divide 6,8 and 12

Answer 1

Prime factorization helps to determine the Least Common Multiple (LCM) of 6, 8 and 12 :
6 = 2 * 3
8 = 2 * 2 * 2
12 = 2 * 2 * 3
LCM (6,8,12) = 2 * 2 * 2 * 3 = 24

Hence, the smallest 3-digit number which meets the requirements must be a multiple of 24. And the smallest 3-digit multiple of 24 is 

24 * 5 = 120.

Answer 2

LCM of 6 = 2 * 3
LCM of 8 = 2^3
LCM of 12 = 2^2 * 3

LCM of 6,8,12 = 2^3 * 3

                       = 24

The Lowest common factor = 2^3 * 3 * 5

                                              = 120

Smallest 3 digit number = 120.


Hope this helps!