Word problem involving the least common multiple of 2 numbers Suppose that hot dogs come in packs of 9 and buns come in packs of 12 . Sam bought the same number of hot dogs as buns. It was the least number of each for which this was possible. Answer the following questions. \( \square \) hot dogs How many hot dogs did he buy? How many packs of buns did he buy? \( \square \) packs

To solve the problem, we first determine the least common multiple (LCM) of 9 and 12. The prime factorization of 9 is \(3^2\) and for 12, it's \(2^2 \times 3^1\). The LCM takes the highest powers of the prime factors: \(2^2\) from 12 and \(3^2\) from 9. Therefore, the LCM of 9 and 12 is \(2^2 \times 3^2 = 4 \times 9 = 36\). Thus, Sam bought \(36\) hot dogs. To find out how many packs of buns he bought, we divide the total buns by the pack size: \(36 \div 12 = 3\) packs. So, Sam bought \(36\) hot dogs and \(3\) packs of buns! 🌭🥖