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Ashley has $18$ commemorative plates and $12$ commemorative spoons. She wants to display them in groups throughout her house, each with the same combination of plates and spoons, with none left over. What is the greatest number of groups Ashley can display? $\newline$ $\_\_\_\_\_\_\_\_\_$ groups

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GCF and LCM: word problems

Full solution

Q. Ashley has

18

commemorative plates and

12

commemorative spoons. She wants to display them in groups throughout her house, each with the same combination of plates and spoons, with none left over. What is the greatest number of groups Ashley can display?

\newline

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

groups

Identify Need: Identify the need to find the greatest common divisor (GCD) to determine the maximum number of groups where each group has the same number of plates and spoons without any leftovers.
Calculate GCD: Calculate the GCD of $18$ (plates) and $12$ (spoons). Factors of $18$ are $1, 2, 3, 6, 9, 18$ . Factors of $12$ are $1, 2, 3, 4, 6, 12$ . The common factors are $1, 2, 3, 6$ . The greatest is $6$ .
Conclude Solution: Conclude that Ashley can create $6$ groups of $3$ plates and $2$ spoons each, since $18$ divided by $6$ equals $3$ and $12$ divided by $6$ equals $2$ .

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