Question

Bill is putting his baseball cards in a binder. For the amount of baseball cards he has, he knows he can use either 5 on each page with none left over, or 9 on each page with none left over. Which is the least amount of baseball cards Bill has?
A.
27
B.
45
C.
90
D.
35

Answer 1

To find the least amount of baseball cards Bill has, we need to determine the least common multiple (LCM) of the two numbers, 5 and 9. The LCM is the smallest positive integer that is divisible by both numbers.

1. **Find the multiples of 5:**
- 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, ...

2. **Find the multiples of 9:**
- 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, ...

3. **Identify the smallest common multiple from these lists:**
- The first common multiple we find is 45.

4. **Check if there are any multiples less than 45:**
- The multiples of 5 below 45 are: 5, 10, 15, 20, 25, 30, 35, 40.
- The multiples of 9 below 45 are: 9, 18, 27, 36, 45.
- None of these are common, so 45 is indeed the least common multiple.

Thus, the least amount of baseball cards Bill has is **45**.

The correct answer is **B. 45**.