Knowee
Questions
Features
Study Tools

Bobby is putting bottles and cans in bags to take to a recycling facility. He puts bottles in bags of 8 and cans in bags of 20, with no partially filled bags. While counting up the cans and bottles, an employee at the recycling facility points out that Bobby has the same number of each. What is the smallest number of bottles that he can recycle?

Question

Bobby is putting bottles and cans in bags to take to a recycling facility. He puts bottles in bags of 8 and cans in bags of 20, with no partially filled bags. While counting up the cans and bottles, an employee at the recycling facility points out that Bobby has the same number of each. What is the smallest number of bottles that he can recycle?

🧐 Not the exact question you are looking for?Go ask a question

Solution

To solve this problem, we need to find the least common multiple (LCM) of the numbers 8 and 20, which represent the number of bottles and cans Bobby can put in each bag, respectively. The LCM of two numbers is the smallest number that is a multiple of both numbers.

Here are the steps to find the LCM of 8 and 20:

  1. Write down the prime factors of each number:

    • The prime factors of 8 are 2, 2, and 2.
    • The prime factors of 20 are 2, 2, and 5.

  2. Write down all the prime factors, without repetition, and the highest power of each factor when it appears in either number:

    • The prime factors are 2 and 5.
    • The highest power of 2 is 3 (because 8 = 2^3), and the highest power of 5 is 1 (because 20 = 2^2 * 5^1).

  3. Multiply these highest powers together:

    • The LCM is 2^3 * 5^1 = 8 * 5 = 40.

So, the smallest number of bottles that Bobby can recycle, such that he has the same number of bottles and cans, is 40.

This problem has been solved

Similar Questions

Meg is putting bottles and cans in bags to take to a recycling facility. She puts bottles in bags of 8 and cans in bags of 7, with no partially filled bags. While counting up the cans and bottles, an employee at the recycling facility points out that Meg has the same number of each. What is the smallest number of bottles that she can recycle?

Choose the correct answer.A shopkeeper packed chocolates into bags of 48 and candies into bags of 150. He packed the same number of chocolates and candies. Find the least number of bags of candies the shopkeeper packed.5 bags of candies8 bags of candies3 bags of candies9 bags of candies

Miko helped fill water bottles for athletes during the school sports meeting. The capacity of a bottle was 528 litres. What is the smallest number of such bottles she needed to hold 14 litres of water?

Ruben wants to create snack bags for a trip he is going on. He has 16 granola bars and 24 pieces of dried fruit. If the snack bags should be identical without any food left over, what is the greatest number of snack bags Ruben can make?

Bobby tutors students in groups of 8. Meanwhile, Polly tutors students in groups of 12. While discussing their work, the tutors realize that they both work with the same total number of students. What is the smallest number of students each can have?

1/3

Upgrade your grade with Knowee

Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.