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Carla buys strawberry gum in packs of $9$ pieces and blueberry gum in packs of $5$ pieces. If Carla wants to buy the same amount of each type of gum, what is the smallest number of pieces of each flavor that she must buy? $\newline$ $\_\_\_\_\_$ pieces

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GCF and LCM: word problems

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Q. Carla buys strawberry gum in packs of

9

pieces and blueberry gum in packs of

5

pieces. If Carla wants to buy the same amount of each type of gum, what is the smallest number of pieces of each flavor that she must buy?

\newline

\_\_\_\_\_

pieces

Identify Problem: Step $1$ : Identify the problem. Carla needs the same number of strawberry and blueberry gum pieces. We need to find the least common multiple (LCM) of the pack sizes.
Determine Pack Sizes: Step $2$ : Determine the pack sizes. Strawberry gum comes in packs of $9$ pieces, and blueberry gum comes in packs of $5$ pieces.
List Multiples: Step $3$ : List the multiples of each pack size to find the LCM. $\newline$ Multiples of $9$ : $9$ , $18$ , $27$ , $36$ , $45$ , $54$ , $63$ , $72$ , $81$ , $9$ $0$ ... $\newline$ Multiples of $9$ $1$ : $9$ $1$ , $9$ $3$ , $9$ $4$ , $9$ $5$ , $9$ $6$ , $9$ $7$ , $9$ $8$ , $9$ $9$ , $45$ , $18$ $1$ ... $\newline$ The smallest common multiple is $45$ .

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