Practice Least Number of Cartons

puremath

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Jan 15, 2020
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I do not understand this question. It is worded so badly. Can you explain what is going on?

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MarkFL

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They are essentially asking for the lowest common multiple (LCM) of 6 and 8. If you don't immediately see this is 24, consider the prime factorization of both numbers:

\(\displaystyle 6=2\cdot3\)

\(\displaystyle 8=2^3\)

Now, we need the greatest number of each prime present in each to make up our LCM:

\(\displaystyle \text{lcm}(6,8)=2^3\cdot3=24\)

We see that 2 and 3 are the primes present in their factorizations. The highest power on 2 is 3 and the highest power on 3 is 1, and so that determines the LCM.
 
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puremath

Active Member
Jan 15, 2020
1,203
12
38
55
Bronx, NY
They are essentially asking for the lowest common multiple (LCM) of 6 and 8. If you don't immediately see this is 24, consider the prime factorization of both numbers:

\(\displaystyle 6=2\cdot3\)

\(\displaystyle 8=2^3\)

Now, we need the greatest number of each prime present in each to make up our LCM:

\(\displaystyle \text{lcm}(6,8)=2^3\cdot3=24\)

We see that 2 and 3 are the primes present in their factorizations. The highest power on 2 is 3 and the highest power on 3 is 1, and so that determines the LCM.
This middle school question is poorly stated, in my opinion. I also got 24 after struggling with the stupidity of this application.