Common Multiples of 6 and 9
In mathematics, the common multiples of two numbers are the numbers that are divisible by both numbers. For example, the common multiples of 6 and 9 are 18, 36, 54, 72, and so on.
To find the common multiples of two numbers, we can use the following steps:
- List the multiples of the larger number.
- Find the multiples of the smaller number that are also multiples of the larger number.
In the case of 6 and 9, the larger number is 9. The multiples of 9 are 9, 18, 27, 36, and so on. The multiples of 6 that are also multiples of 9 are 18, 36, and so on.
Therefore, the common multiples of 6 and 9 are 18, 36, 54, 72, and so on.
Questions and Answers
What is the least common multiple of 6 and 9?
Answer: The least common multiple of two numbers is the smallest number that is divisible by both numbers. In the case of 6 and 9, the least common multiple is 18.
What are the first six common multiples of 6 and 9?
Answer: The first six common multiples of 6 and 9 are 18, 36, 54, 72, 90, and 108.
How can we find the common multiples of any two numbers?
Answer: To find the common multiples of two numbers, we can use the following steps:
- List the multiples of the larger number.
- Find the multiples of the smaller number that are also multiples of the larger number.
For example, to find the common multiples of 12 and 15, we would list the multiples of 15, which are 15, 30, 45, 60, and so on. We would then find the multiples of 12 that are also multiples of 15. These are 12, 30, and 60. Therefore, the common multiples of 12 and 15 are 12, 30, and 60.
Applications of Common Multiples
Common multiples have a variety of applications in mathematics and everyday life. For example, they can be used to:
- Determine the number of times a certain event occurs in a given time period.
- Calculate the length of a repeating pattern.
- Divide a number into equal groups.
For example, we can use common multiples to determine the number of times a train arrives at a station every day. If the train arrives every 6 hours and the day has 24 hours, then the train arrives 24 / 6 = 4 times per day.
We can also use common multiples to calculate the length of a repeating pattern. For example, if a pattern repeats every 6 seconds and we want to know how long it takes for the pattern to repeat 10 times, then we can use the common multiple of 6 and 10, which is 30. Therefore, the pattern will repeat 10 times in 30 seconds.
Finally, we can use common multiples to divide a number into equal groups. For example, if we have 36 apples and we want to divide them into groups of 6, then we can use the common multiple of 36 and 6, which is 36. Therefore, we can divide the apples into 6 groups of 6.
