QuestionFind how many days until the field hockey team (every 4 days) and soccer team (every 6 days) share the field again. Use LCM.

Studdy Solution

STEP 1

Assumptions1. The field hockey team uses the field every4 days. . The soccer team uses the field every6 days.
3. We are looking for the least common multiple (LCM) of4 and6, which represents the number of days after which both teams will share the field again.

STEP 2

First, we need to find the prime factors of4 and6.For4, the prime factors are $4 =2 \times2$ For6, the prime factors are $6 =2 \times$

STEP 3

Now, we find the least common multiple (LCM) of and6. The LCM is the product of the highest powers of all primes appearing in either number.
The prime factors appearing in either or6 are2 and3.
The highest power of2 appearing in either or6 is $2^2$ (from).
The highest power of3 appearing in either or6 is $3^1$ (from6).

STEP 4

So, the LCM of4 and6 is the product of the highest powers of all primes appearing in either number, which is $2^2 \times3^1$ .
$LCM =2^2 \times3^1$

STEP 5

Calculate the LCM.
$LCM =2^2 \times3^1 =4 \times3 =12$ So, the field hockey team and the soccer team will share the field again12 days after their last practice.

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