The number of boxes in a warehouse can be divided evenly...

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The number of boxes in a warehouse can be divided evenly into 6 equal shipments by boat or 27 equal shipments by truck. What is the smallest number of boxes that could be in the warehouse?

A. 27
B. 33
C. 54
D. 81
E. 162

The OA is C.

I don't have clear this PS question. I appreciate if any expert explains it to me. Thank you so much.
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by JayaSrinivasK » Mon Feb 26, 2018 3:54 pm

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by Brent@GMATPrepNow » Tue Feb 27, 2018 7:12 am
AAPL wrote:The number of boxes in a warehouse can be divided evenly into 6 equal shipments by boat or 27 equal shipments by truck. What is the smallest number of boxes that could be in the warehouse?

A. 27
B. 33
C. 54
D. 81
E. 162
Let N = the number of boxes in the warehouse

If the boxes in a warehouse can be divided evenly into 6 equal shipments (by boat), then N is divisible by 6
If the boxes in a warehouse can be divided evenly into 27 equal shipments (by truck), then N is divisible by 27

What is the smallest number of boxes that could be in the warehouse?
So, we're looking for the LEAST COMMON MULTIPLE (LCM) of 6 and 27

From here, one approach is to just check the the answer choices, starting from A.
A. 27 is not a multiple of 6. ELIMINATE
B. 33 is not a multiple of 6. ELIMINATE
C. 54 IS a multiple of both 6 and 27. So, the correct answer must be C


Approach #2:
6 = (2)(3)
27 = (3)(3)(3)
So, the LCM must have ONE 2 and THREE 3's
In other words, LCM = (2)(3)(3)(3) = 54
Answer: C

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by Scott@TargetTestPrep » Wed Feb 28, 2018 10:28 am
AAPL wrote:The number of boxes in a warehouse can be divided evenly into 6 equal shipments by boat or 27 equal shipments by truck. What is the smallest number of boxes that could be in the warehouse?

A. 27
B. 33
C. 54
D. 81
E. 162
To solve, we just need to determine the least common multiple of 6 and 27, which is 54.

Answer: C

Scott Woodbury-Stewart
Founder and CEO
[email protected]

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