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Bob is buying pens and pencils from the store. Pens come in packages of $2$ , but pencils are sold in packages of $3$ . If Bob wishes to purchase the same number of pens as pencils, what is the smallest number of pens that he can buy? $\newline$ $\_\_\_\_\_$ pens

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GCF and LCM: word problems

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Q. Bob is buying pens and pencils from the store. Pens come in packages of

2

, but pencils are sold in packages of

3

. If Bob wishes to purchase the same number of pens as pencils, what is the smallest number of pens that he can buy?

\newline

\_\_\_\_\_

pens

Identify the problem: Step $1$ : Identify the problem. Bob needs the same number of pens as pencils. Pens are in packs of $2$ , and pencils are in packs of $3$ .
Find the LCM: Step $2$ : Find the Least Common Multiple (LCM) of the package sizes to ensure Bob buys equal numbers of pens and pencils. Calculate LCM of $2$ and $3$ .
List multiples: Step $3$ : List multiples of $2$ ( $2, 4, 6, 8, 10, \ldots$ ) and $3$ ( $3, 6, 9, 12, \ldots$ ). The smallest common multiple is $6$ .
Calculate number of pens: Step $4$ : Since pens come in packages of $2$ , divide the LCM by the package size to find the number of pens. $6 \div 2 = 3$ pens.

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