Khan/khan-exercises — Issue #8968: Least common multiple and greatest common divisor word problems - LCM / GCD Question wording
Author: KhanBugz
Created: 2011-12-19 14:04:56+00:00
State: open
Labels: chrome, win7, wrong-or-unclear

Reporter: swptl@live.com

My suggestion is in reference to this Khan Academy question and answer:
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Next week, Nadia is having a party, and she plans to serve hot dogs in buns. She does not want to have any food left over.

Hot dogs come in packages of 30, and buns come in packages of 18.

What is the minimum amount of hot dogs and buns Nadia can buy?

To find the minimum amount of hot dogs and buns Nadia can buy, we need to find the least common multiple of the number of hot dogs per package (30) and the number of buns per package (18).

The least common multiple is the smallest number that is a multiple of 30 and 18.

We know that 30 x 18 (or 540) is a common multiple, but is it the least common multiple?

Write out the multiples of 30 until we find a number divisible by 18.

30, 60, 90

So, 90 is the least common multiple of 30 and 18.

The smallest amount of food Nadia can buy is 90 hot dogs and buns, or 3 packages of hot dogs and 5 packages of buns.
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The answer to this question (with the way this question is worded) is: 30 hot dogs and 18 hot dog buns or one package of each.

The question should have been worded:

What's the least amount of hot dogs that Nadia can buy, if Nadia must have an exact match with the number of hot dogs to the number of hot dog buns?

Thank you,

Steve W.

[least_common_multiple_and_greatest_common_divisor_word_problems.html?seed=157&problem=lcm-uniforms](http://sandcastle.khanacademy.org/media/castles/Khan:master/exercises/least_common_multiple_and_greatest_common_divisor_word_problems.html?seed=157&problem=lcm-uniforms&debug)

[Answer timeline](http://sandcastle.khanacademy.org/media/castles/Khan:master/exercises/least_common_multiple_and_greatest_common_divisor_word_problems.html?seed=157&problem=lcm-uniforms&debug&activity=%5B%5D)

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