I agree with the answer given above, but I disagree with the analysis.
The question:
M is a 3-digit positive integer, and the product of the three digits is 144. What is the unit's digit of M when M has the least value?
(A) 2
(B) 4
(C) 6
(D) 8
(E) 9
Well, there are a few different ways to make a product of 144 from three single-digit integers, including 144 = [spoiler]4*4*9[/spoiler], 144 = [spoiler]4*6*6[/spoiler], or 144 = [spoiler]2*8*9[/spoiler]. Because
2 is a possible choice of digit, the smallest value of M has to have
2 as the hundreds digit.
Given a hundred digit of
2, the other two digits must be
8 and
9. To make the number as small as possible, the order has to be:
289.
Thus, the units digit is
9 --- Answer Choice =
E.
I hope
sam2304 and others appreciate that I spoilered the bejeebers out of this response. BTW,
sam2304, I like the fact that the number in your screenname is a perfect square -- 48^2 = 2304.
Please let me know if any one has any questions on my analysis.
Mike
