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While performing a piece of music, Gary strikes the cymbals every $10$ beats and the triangle is every $6$ beats. If he just struck both at the same time, how many beats will pass before he again strikes them at the same time? $\newline$ _____ beats

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GCF and LCM: word problems

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Q. While performing a piece of music, Gary strikes the cymbals every

10

beats and the triangle is every

6

beats. If he just struck both at the same time, how many beats will pass before he again strikes them at the same time?

\newline

_____ beats

Identify Intervals: Step $1$ : Identify the intervals at which Gary strikes the cymbals and the triangle. $\newline$ Cymbals: every $10$ beats. $\newline$ Triangle: every $6$ beats.
Find LCM: Step $2$ : Find the Least Common Multiple (LCM) of $10$ and $6$ to determine when Gary will strike both instruments together again. $\newline$ Factors of $10$ : $1$ , $2$ , $5$ , $10$ . $\newline$ Factors of $6$ : $1$ , $2$ , $6$ $0$ , $6$ . $\newline$ Common multiples of $10$ and $6$ are $6$ $4$ , $6$ $5$ , $6$ $6$ , etc. $\newline$ The smallest common multiple is $6$ $4$ .

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