Final answer:
Stefan should find the least common multiple of 10 and 12, which is 60, to prevent having any leftover supplies. So, he should purchase 6 packs of buckles and 5 packs of straps to have a total of 60 buckles and straps each.
Step-by-step explanation:
The student is asking about finding the least common multiple (LCM) of two numbers in a practical scenario, specifically for pairing dog collar straps with buckles. In this problem, Stefan has packs of 10 buckles and 12 straps and he wants to ensure that he has the same number of buckles and straps without any leftovers. To find the smallest number of each he should purchase, we need to calculate the LCM of 10 and 12.
- First, we list the multiples of 10 and 12:
- Multiples of 10: 10, 20, 30, 40, 50, 60, ...
- Multiples of 12: 12, 24, 36, 48, 60, ...
Next, we identify the least common multiple among these numbers, which is 60. Therefore, Stefan should purchase enough packs to provide him with 60 buckles and 60 straps.
Since there are 10 buckles in a pack, he would need to purchase 6 packs of buckles (6 packs × 10 buckles per pack = 60 buckles). Similarly, since there are 12 straps in a pack, he would need 5 packs of straps (5 packs × 12 straps per pack = 60 straps). The correct answer to the question is a) 60.