Question

kamals sports sells golf tees in packs of 8. meanwhile, candices gear sells them in packs of 6. if both shops sold the same number of golf tees this week, what is the smallest number of tees each could have sold?

Explanation:

Step1: Find the least common multiple (LCM)

To find the smallest number of tees that both shops could have sold (where one sells in packs of 8 and the other in packs of 6), we need to find the LCM of 8 and 6.
Prime - factorize the numbers:

• \(8 = 2\times2\times2\)
• \(6=2\times3\)

The LCM is calculated by taking the highest power of each prime factor present in the factorizations.
For the prime factor 2, the highest power is \(2^{3}\) (from 8), and for the prime factor 3, the highest power is \(3^{1}\) (from 6).

Step2: Calculate the LCM

Using the formula \(LCM(a,b)=\frac{a\times b}{GCD(a,b)}\) (where \(GCD\) is the greatest common divisor). First, find the \(GCD\) of 8 and 6.
The factors of 8 are 1, 2, 4, 8. The factors of 6 are 1, 2, 3, 6. So \(GCD(8,6) = 2\).
Then \(LCM(8,6)=\frac{8\times6}{2}=\frac{48}{2}=24\).
Another way using prime - factorization: \(LCM(8,6)=2^{3}\times3^{1}=8\times3 = 24\)

Answer:

24