number properties

[sud21]

M is a 3 digit positive integer. Product of the 3 digits is 144. We have to select three digits 0 to 9, taking digits in such a way that the higher digits are taken so that it fits into 3 digits.
So 144=9.4.4. Least value=449. Units digit is 9.

[sam2304]

Use spoiler for explanations.

[Mike@Magoosh]

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

[neelgandham]

BTW, sam2304, I like the fact that the number in your screenname is a perfect square -- 48^2 = 2304.

Great observation Doc !!