A geometry class has a pizza party. there are 14 students that have a pizza. Each pizza has 8 slices. The teacher wants to buy the least number of pizzas so that they are the same number of slices for each student. (I know the answers, but I don't know how to show the work.)
How many pizzas should be purchased?
How many slices would each student receive?
To find out how many pizzas should be purchased, we need to determine the least common multiple (LCM) of the number of slices and the number of students.
1. Start by finding the LCM of 8 (number of slices per pizza) and 14 (number of students).
- The prime factorization of 8 is 2 * 2 * 2.
- The prime factorization of 14 is 2 * 7.
2. Identify the common prime factors of both numbers. In this case, the common factor is only 2.
3. Take the highest exponent of each prime factor. Since 8 has three 2s and 14 has one 2, we take the highest exponent of 2, which is 3.
4. Multiply all the prime factors with the highest exponents together. In this case, it is 2 * 2 * 2 * 7 = 56.
Therefore, the LCM of 8 and 14 is 56.
Now let's use the LCM to find out how many slices each student would receive:
To find out how many slices each student would receive, divide the total number of slices (56) by the number of students (14).
56 slices ÷ 14 students = 4 slices per student.
So, the teacher should purchase 56 slices in order to have an equal number of slices for each student, and each student would receive 4 slices.