Question

while performing a piece of music, jim strikes the cymbals every 2 beats and the triangle is every 12 beats. if he just struck both at the same time, how many beats will pass before he again strikes them at the same time? beats

Explanation:

Step1: Identify the problem type

This is a problem of finding the least common multiple (LCM) of two numbers, 2 and 12, as we need to find the smallest number of beats after which both the cymbals (struck every 2 beats) and the triangle (struck every 12 beats) are struck at the same time again.

Step2: Recall the LCM formula for two numbers

If we have two numbers \(a\) and \(b\), and we know that \(b\) is a multiple of \(a\) (i.e., \(b = k\times a\) for some integer \(k\)), then the LCM of \(a\) and \(b\) is \(b\) itself.

Step3: Check the relationship between 2 and 12

We can see that \(12=6\times2\), which means 12 is a multiple of 2.

Step4: Determine the LCM

Since 12 is a multiple of 2, the least common multiple of 2 and 12 is 12.

Answer:

12