To solve this problem, we need to find the least common multiple (LCM) of the numbers 5 and 9. The LCM of two numbers is the smallest number that is a multiple of both numbers.

Here are the steps to find the LCM:

1. List the prime factors of each number:
- The prime factors of 5 are: 5
- The prime factors of 9 are: 3, 3

2. For each prime number that appears in either list, count the number of times it appears in each list. Take the maximum count for each prime number.

- The prime number 5 appears once in the first list and not at all in the second list. So, the maximum count for 5 is 1.
- The prime number 3 appears twice in the second list and not at all in the first list. So, the maximum count for 3 is 2.

3. Multiply each prime number by the maximum count from step 2. Then multiply these results together to get the LCM.

- Multiply 5 (from the first list) by 1 (its maximum count): 5 * 1 = 5
- Multiply 3 (from the second list) by 2 (its maximum count): 3 * 3 = 9
- Multiply these results together: 5 * 9 = 45

So, the smallest number of books each could have shelved is 45.

Question

To solve this problem, we need to find the least common multiple (LCM) of the numbers 5 and 9. The LCM of two numbers is the smallest number that is a multiple of both numbers.

Here are the steps to find the LCM:

1. List the prime factors of each number:
   - The prime factors of 5 are: 5
   - The prime factors of 9 are: 3, 3

2. For each prime number that appears in either list, count the number of times it appears in each list. Take the maximum count for each prime number.

- The prime number 5 appears once in the first list and not at all in the second list. So, the maximum count for 5 is 1.
   - The prime number 3 appears twice in the second list and not at all in the first list. So, the maximum count for 3 is 2.

3. Multiply each prime number by the maximum count from step 2. Then multiply these results together to get the LCM.

- Multiply 5 (from the first list) by 1 (its maximum count): 5 * 1 = 5
   - Multiply 3 (from the second list) by 2 (its maximum count): 3 * 3 = 9
   - Multiply these results together: 5 * 9 = 45

So, the smallest number of books each could have shelved is 45.

Knowee AI · Accepted Answer

To solve this problem, we need to find the least common multiple (LCM) of the numbers 5 and 9. The LCM of two numbers is the smallest number that is a multiple of both numbers.

Here are the steps to find the LCM:

1. List the prime factors of each number:
   - The prime factors of 5 are: 5
   - The prime factors of 9 are: 3, 3

2. For each prime number that appears in either list, count the number of times it appears in each list. Take the maximum count for each prime number.

- The prime number 5 appears once in the first list and not at all in the second list. So, the maximum count for 5 is 1.
   - The prime number 3 appears twice in the second list and not at all in the first list. So, the maximum count for 3 is 2.

3. Multiply each prime number by the maximum count from step 2. Then multiply these results together to get the LCM.

- Multiply 5 (from the first list) by 1 (its maximum count): 5 * 1 = 5
   - Multiply 3 (from the second list) by 2 (its maximum count): 3 * 3 = 9
   - Multiply these results together: 5 * 9 = 45

So, the smallest number of books each could have shelved is 45.

Sharon and Mateo are shelving books at a public library. Sharon shelves 5 books at a time, whereas Mateo shelves 9 at a time. If they end up shelving the same number of books, what is the smallest number of books each could have shelved?

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