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

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We first determine the least common multiple of $$9$$ and $$12$$.

1. Factorize each number:
   - $$9 = 3^2$$
   - $$12 = 2^2 \times 3$$

2. The LCM is obtained by taking the highest power of each prime:
   $$
   \text{lcm}(9,12) = 2^2 \times 3^2 = 4 \times 9 = 36
   $$

3. The LCM $$36$$ represents the number of hot dogs (and buns) Sam bought.

4. To find the number of packs:
   - Hot dogs come in packs of $$9$$:
     $$
     \text{Packs of hot dogs} = \frac{36}{9} = 4
     $$
   - Buns come in packs of $$12$$:
     $$
     \text{Packs of buns} = \frac{36}{12} = 3
     $$

Thus, Sam bought $$36$$ hot dogs and $$3$$ packs of buns.
Sam bought 36 hot dogs and 3 packs of buns.

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