# PracticeLeast Number of Cartons

#### puremath

##### Active Member
I do not understand this question. It is worded so badly. Can you explain what is going on?

#### MarkFL

##### La Villa Strangiato
Staff member
Moderator
Math Helper
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.

Jason and puremath

#### puremath

##### Active Member
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.