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One day, Aiden and his friends had lunch while sitting at tables of $10$ . Another day, they had lunch at tables of $5$ . What is the smallest number of people that could be in the group? $\newline$ $\_\_\_\_\_$ people

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GCF and LCM: word problems

Full solution

Q. One day, Aiden and his friends had lunch while sitting at tables of

10

. Another day, they had lunch at tables of

5

. What is the smallest number of people that could be in the group?

\newline

\_\_\_\_\_

people

Identify Requirement: Identify the problem's requirement. $\newline$ We need to find the smallest number of people that can fit perfectly at tables of both $10$ and $5$ .
Mathematical Approach: Determine the mathematical approach. $\newline$ We need the Least Common Multiple (LCM) of $10$ and $5$ to ensure no one is left without a seat.
Calculate LCM: Calculate the LCM of $10$ and $5$ . $\newline$ $10$ : $1$ , $2$ , $5$ , $10$ $\newline$ $5$ : $1$ , $5$ $\newline$ Common multiple is $10$ .
Verify Calculation: Verify the calculation. $\newline$ LCM of $10$ and $5$ is indeed $10$ , as both $10$ and $5$ divide $10$ without any remainder.

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