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At a school event, adults are seated in groups of exactly $6$ and children are seated in groups of exactly $3$ . If there are the same number of adults as children, what is the minimum number of adults attending? $\newline$ $\_\_\_\_\_\_$ adults

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GCF and LCM: word problems

Full solution

Q. At a school event, adults are seated in groups of exactly

6

and children are seated in groups of exactly

3

. If there are the same number of adults as children, what is the minimum number of adults attending?

\newline

\_\_\_\_\_\_

adults

Identify seating arrangement: Step $1$ : Identify the seating arrangement. $\newline$ Adults are seated in groups of $6$ , and children are seated in groups of $3$ . Since there are equal numbers of adults and children, we need to find the smallest number that is both a multiple of $6$ and $3$ .
Calculate LCM: Step $2$ : Calculate the Least Common Multiple (LCM) of $6$ and $3$ . The multiples of $6$ are: $6, 12, 18, 24, \ldots$ The multiples of $3$ are: $3, 6, 9, 12, 15, 18, \ldots$ The smallest common multiple is $6$ .
Determine minimum adults: Step $3$ : Determine the minimum number of adults. $\newline$ Since each group of adults must have exactly $6$ adults, and the LCM is $6$ , the minimum number of adults is $6$ .

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