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By coincidence, Luther's Obedience School trained the same number of dogs and cats last week. The school teaches dogs in groups of $10$ and cats in groups of $5$ . What is the smallest number of cats the school could have had? $\newline$ $\_\_\_\_\_\_\_\_\_$ cats

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GCF and LCM: word problems

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Q. By coincidence, Luther's Obedience School trained the same number of dogs and cats last week. The school teaches dogs in groups of

10

and cats in groups of

5

. What is the smallest number of cats the school could have had?

\newline

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

cats

Find LCM: Determine the Least Common Multiple (LCM) of the group sizes for dogs and cats to find the smallest number of each that could be equally divided into groups. Dogs are taught in groups of $10$ and cats in groups of $5$ .
Calculate Cats: Since the LCM of the group sizes is $10$ , and each group of cats contains $5$ cats, the smallest number of cats that could be taught is twice the number of groups, as each group contains $5$ cats.

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