what is the least number of dancers that are needed if a choreographer wants to arrange them in groups of 4,5, or 6 with none left?
im not understanding the question. can you help?
You're looking for the greatest common multiple of 4, 5, and 6
Which of these multiples of 6 is also a multiple of 4 and 5?
6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72
60
so the least number of dancers that are needed for groups of 4,5,6 is
60
Of course! Let's break down the question step by step.
The choreographer wants to arrange the dancers in groups of 4, 5, or 6. This means that each group should consist of either 4, 5, or 6 dancers, without any dancers left ungrouped.
To find the least number of dancers required, we need to find the least common multiple (LCM) of 4, 5, and 6. The LCM is the smallest number that is divisible by all of the given numbers.
Here are the steps to find the LCM of 4, 5, and 6:
1. List the multiples of each number until you find a common multiple. For 4, the multiples are: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, ... For 5, the multiples are: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, ... For 6, the multiples are: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, ...
2. Find the smallest number that appears in all three lists. In this case, 60 is the smallest number that is divisible by 4, 5, and 6 without leaving a remainder.
Therefore, the least number of dancers that are needed to form groups of 4, 5, or 6 with none left over is 60. Keep in mind that there may be other larger numbers that also meet this criteria, but we are looking for the least possible number.