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Suppose the number is n

Then n = 16x + 2 for some non-negative integer x

and n = 18y + 12 for some non-negative integer y.

That gives 16x + 2 = 18y + 12

which can be simplified to 8x = 9y + 5

or x = (9y + 5)/8

Since x is an integer, 8 must go into 9y+5 evenly.

That requires that 9y leaves a remainder of 3 when divided by 8.

Since 9 and 8 are coprime, y = 3

So n = 18*3 + 12 54+12 = 66

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