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QuestionWhen will both the soccer team (every 3 days) and basketball team (every 5 days) play on the same day again? A. 3 days B. 6 days C. 15 days D. 18 days

Studdy Solution

STEP 1

Assumptions1. The soccer team plays every3 days. . The basketball team plays every5 days.
3. We are looking for the least common multiple (LCM) of3 and5, which represents the number of days until both teams play on the same day again.

STEP 2

To find the LCM of two numbers, we can use the formulaLCM(a,b)=∣a×b∣gcd(a,b)LCM(a, b) = \frac{|a \times b|}{gcd(a, b)}where gcd(a,b)gcd(a, b) is the greatest common divisor of aa and bb.

STEP 3

In this case, a=3a =3 (the soccer team's play cycle) and b=5b =5 (the basketball team's play cycle). So, we need to find gcd(3,5)gcd(3,5).

STEP 4

Since3 and are both prime numbers, their greatest common divisor is1.
gcd(3,)=1gcd(3,) =1

STEP 5

Now, we can calculate the LCM.
LCM(3,5)=∣3×5∣gcd(3,5)LCM(3,5) = \frac{|3 \times5|}{gcd(3,5)}

STEP 6

Substitute the values into the LCM formula.
LCM(3,5)=∣3×5∣1LCM(3,5) = \frac{|3 \times5|}{1}

STEP 7

Calculate the LCM.
LCM(3,5)=151=15LCM(3,5) = \frac{15}{1} =15So, both teams will have games on the same day again in15 days. The correct answer is C. In15 days.

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