If you happen to be viewing the article Six bells Commence Tolling together and Toll at intervals of 2, 4, 6, 8, 10 and 12 seconds respectively. In 30 minutes, how many Times do they Toll together?? on the website Math Hello Kitty, there are a couple of convenient ways for you to navigate through the content. You have the option to simply scroll down and leisurely read each section at your own pace. Alternatively, if you’re in a rush or looking for specific information, you can swiftly click on the table of contents provided. This will instantly direct you to the exact section that contains the information you need most urgently.
Have you ever wondered how six bells, each with its own rhythm (2, 4, 6, 8, 10, and 12 seconds), chime together? Let’s figure out how many times they do it in just 30 minutes!
Six bells Commence Tolling together and Toll at intervals of 2, 4, 6, 8, 10 and 12 seconds respectively. In 30 minutes, How many times do they Toll together?
They will toll 15 times in 30 minutes.
Explanation
To find out how many times the six bells toll together in 30 minutes, we need to determine the time it takes for all six bells to toll at the same time again. This time is known as the least common multiple (LCM) of the intervals between tolls.
The given intervals are 2, 4, 6, 8, 10, and 12 seconds.
First, find the prime factorization of each interval:
- 2 seconds: 2
- 4 seconds: 2^2
- 6 seconds: 2 * 3
- 8 seconds: 2^3
- 10 seconds: 2 * 5
- 12 seconds: 2^2 * 3
Now, find the LCM by taking the highest power of each prime factor:
LCM = 2^3 * 3 * 5 = 120 seconds
So, the bells toll together every 120 seconds. Now, convert 30 minutes to seconds:
30 minutes * 60 seconds/minute = 1800 seconds
Finally, divide the total time (1800 seconds) by the LCM (120 seconds):
1800 seconds / 120 seconds = 15
Therefore, the six bells will toll together 15 times in 30 minutes.
What is Least Common Multiple?
The Least Common Multiple (LCM) of two or more integers is the smallest positive integer that is divisible by each of the given integers without leaving a remainder. In other words, it is the smallest common multiple shared by those numbers.
For example, consider the numbers 4 and 6. The multiples of 4 are 4, 8, 12, 16, 20, 24, and so on. The multiples of 6 are 6, 12, 18, 24, 30, and so on. The smallest number that appears in both lists is 12. Therefore, the LCM of 4 and 6 is 12.
The LCM is often used in various mathematical and arithmetic applications, such as solving equations with fractions or working with ratios. It is an important concept in number theory and has practical applications in areas like scheduling, where it helps find the least common multiple of different time intervals.
Thank you so much for taking the time to read the article titled Six bells Commence Tolling together and Toll at intervals of 2, 4, 6, 8, 10 and 12 seconds respectively. In 30 minutes, how many Times do they Toll together? written by Math Hello Kitty. Your support means a lot to us! We are glad that you found this article useful. If you have any feedback or thoughts, we would love to hear from you. Don’t forget to leave a comment and review on our website to help introduce it to others. Once again, we sincerely appreciate your support and thank you for being a valued reader!
Source: Math Hello Kitty
Categories: Math
