To find the least number of strands in the package of embroidery floss that can be shared equally among 3, 5, or 6 friends, we need to determine the least common multiple (LCM) of these numbers.
- Finding the LCM of 3, 5, and 6:
- The prime factorization of the numbers:
- \(3 = 3^1\)
- \(5 = 5^1\)
- \(6 = 2^1 \times 3^1\)
To find the LCM, we take the highest power of each prime factor:
- For \(2\), the highest power is \(2^1\) (from 6).
- For \(3\), the highest power is \(3^1\) (from 3 and 6).
- For \(5\), the highest power is \(5^1\) (from 5).
So, \[ \text{LCM} = 2^1 \times 3^1 \times 5^1 = 2 \times 3 \times 5 = 30 \]
Thus, the least number of strands the package can have is 30.
- Considering the condition of sharing equally among 2 friends:
Now, we must check if 30 can also be divided equally among 2 friends.
To check this, we simply divide 30 by 2: \[ 30 \div 2 = 15 \] Since 15 is an integer, 30 can be shared equally among 2 friends.
Therefore, the same answer (30 strands) holds true whether or not we include sharing among 2 friends.
In conclusion:
- The least number of strands the packet can have is 30.
- Adding the condition of equal sharing among 2 friends does not change the answer; 30 is still the least common multiple that accommodates all conditions.