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Sue and Ann went to the amusement park. They bought the same number of ride tickets, but Sue bought them in packs of $9$ , and Ann bought them in packs of $6$ . What is the smallest possible number of tickets they each bought? $\newline$ $\_\_$ tickets

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GCF and LCM: word problems

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Q. Sue and Ann went to the amusement park. They bought the same number of ride tickets, but Sue bought them in packs of

9

, and Ann bought them in packs of

6

. What is the smallest possible number of tickets they each bought?

\newline

\_\_

tickets

Identify Problem: Identify the problem: We need to find the smallest number of tickets Sue and Ann could have bought if Sue bought tickets in packs of $9$ and Ann in packs of $6$ .
Determine Approach: Determine the mathematical approach: Since they bought the same number of tickets, we need to find the Least Common Multiple (LCM) of the pack sizes, $9$ and $6$ .
Calculate LCM: Calculate the LCM: $\newline$ Factors of $9$ : $1, 3, 9$ $\newline$ Factors of $6$ : $1, 2, 3, 6$ $\newline$ Common factors: $3$ $\newline$ LCM calculation: $9$ is $3^2$ and $6$ is $2 \times 3$ . LCM is $2 \times 3^2 = 18$ .

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