Joe works on an assembly line that fills boxes with various toy trinkets. Every sixth box gets a red ball and every eighth box gets a blue whistle. How often does a box get both a red ball and a blue whistle?
Hint least common multiple
Can someone please explain this to me i know what a least common multiple is but i don't understand. I believe that the answer is 24?
Multiples of 6: 6, 12, 18, 24
Multiples of 8: 8, 16, 24
Yes, 24 is the the least common multiple. So every 24th box will get both a red ball and a blue whistle.
To solve this problem, we need to find the least common multiple (LCM) of 6 and 8. The LCM is the smallest number that is divisible by both 6 and 8.
To find the LCM, we can list the multiples of each number and look for the first common multiple.
Multiples of 6: 6, 12, 18, 24, ...
Multiples of 8: 8, 16, 24, ...
From the lists above, we can see that the first common multiple of 6 and 8 is 24. So, every 24th box will have both a red ball and a blue whistle.
Therefore, the correct answer is that a box gets both a red ball and a blue whistle every 24 boxes, not 2 boxes as mentioned in the question.
If you want to verify this, you can take the multiples of 6 and 8 further beyond 24 and see that the next common multiple is 48, which means it happens after every 48 boxes, which confirms that the correct answer is indeed 24.
To answer the question, we need to find the least common multiple (LCM) of 6 and 8.
The LCM is the smallest positive integer that is divisible by both 6 and 8.
To find the LCM, we can write out the multiples of each number until we find a common multiple.
The multiples of 6 are: 6, 12, 18, 24, 30, 36, ...
The multiples of 8 are: 8, 16, 24, 32, 40, 48, ...
You can see that 24 is the smallest number that appears in the list of multiples of both 6 and 8.
So, the LCM of 6 and 8 is 24.
This means that every 24th box will have both a red ball (every 6th box) and a blue whistle (every 8th box).