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Jim and Mabel are studying a set of new words for Spanish class. Jim decides to break the set into lists of $7$ words. Meanwhile, Mabel creates lists of $8$ words. What is the smallest number of words there could be? $\newline$ $\_\_\_\_\_$ words

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GCF and LCM: word problems

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Q. Jim and Mabel are studying a set of new words for Spanish class. Jim decides to break the set into lists of

7

words. Meanwhile, Mabel creates lists of

8

words. What is the smallest number of words there could be?

\newline

\_\_\_\_\_

words

Find LCM: We need to find the smallest number of words that can be divided into both $7$ -word lists and $8$ -word lists without any remainder. This requires finding the Least Common Multiple (LCM) of $7$ and $8$ .
Calculate LCM: Calculate the LCM of $7$ and $8$ . Since $7$ and $8$ are both prime numbers relative to each other (no common factors other than $1$ ), the LCM is simply their product: $7 \times 8 = 56$ .
Final Result: Therefore, the smallest number of words that can be divided into lists of $7$ and $8$ without leftovers is $56$ .

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