Posted by Ever found yourself scratching your head trying to figure out when two different events will happen at the same time? Maybe you’re coordinating a potluck and need to know when both your friends who bring snacks and the ones who bring drinks will arrive together. That’s where understanding multiples, and especially common multiples, comes in handy!
Think of multiples as counting by a certain number. For example, multiples of 2 are 2, 4, 6, 8, and so on. Today, we’re going to explore multiples, focusing on finding the common ground those numbers that appear in the multiples of both 6 and 9. It’s easier than you think, and super useful in everyday life.
Discovering What are the Common Multiples of 6 and 9
Let’s start by listing the multiples of 6. We have: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, and so on. Just keep adding 6 to the previous number. Its like counting by sixes. This is a fundamental skill for grasping the concept of shared multiples.
Now, let’s list the multiples of 9: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, and so on. Notice anything familiar? Yep, some numbers appear in both lists. The first few that stand out are 18, 36, and 54. These are the common multiples!
The smallest of the common multiples is called the Least Common Multiple (LCM). In this case, the LCM of 6 and 9 is 18. This is the first point where the “6 times table” and the “9 times table” intersect. Knowing the LCM can simplify a lot of math problems.
Finding common multiples is incredibly useful when you’re working with fractions. Imagine you need to add 1/6 and 1/9. To do that, you need a common denominator. Guess what? The common multiples of 6 and 9 are exactly what you need to find that common denominator!
Another cool trick is to simply multiply the two numbers (6 and 9 in this case). 6 x 9 = 54. While this always gives you a common multiple, it might not be the least common multiple. So, you can use this to quickly find a common multiple, then check if a smaller number also works.
So, there you have it! Finding the common multiples of 6 and 9 is all about listing out the multiples of each number and seeing where they overlap. Understanding this concept opens doors to easier fraction calculations, smoother project planning, and a deeper understanding of how numbers relate to each other. Why not try finding the common multiples of other number pairs too?