A group of friends get together to make
friendship bracelets. A package of embroidery
floss can be shared equally among 3, 5, or 6 friends
with no strands left over. What is the least number
of strands the package can contain?
b) Suppose the package in part a could also
be shared equally between 2 friends. Does this
change your answer to part a? Why or why not?
must be the smallest number wich divides evenly be 3, 5, and 6
that is , the LCM
it would be 30
b) surely you can answer that part.
To find the least number of strands the package can contain, we need to find the least common multiple (LCM) of the given numbers: 3, 5, and 6.
a) To find the LCM of 3, 5, and 6, we can use the prime factorization method. First, let's factorize each number:
3 = 3^1
5 = 5^1
6 = 2^1 * 3^1
Next, we find the highest power of each prime factor. The highest power of 2 is 1, and the highest power of 3 is also 1. There are no 5s in the prime factorization of 6, so we take 5^1 as well.
Now, we multiply these highest powers:
2^1 * 3^1 * 5^1 = 2 * 3 * 5 = 30
Therefore, the least number of strands the package can contain is 30.
b) If the package could also be shared equally between 2 friends, this does not change the answer to part a. The least number of strands the package can contain is still 30. This is because 2 is already a factor of 6, which is included in the calculation for the LCM of 3, 5, and 6. Adding the possibility of sharing equally between 2 friends doesn't introduce any new prime factors, thus the LCM remains the same.
To find the least number of strands in the package, we need to find the least common multiple (LCM) of 3, 5, and 6.
a) LCM(3, 5, 6) = 30
Therefore, the least number of strands the package can contain is 30.
b) In part a, the package could not be shared equally between 2 friends. The LCM of 3, 5, and 6 is 30, which means that the package can only be shared equally among 3, 5, or 6 friends. So, the answer to part a does not change.