What Is The Least Common Multiple Of 9 And 7?

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Introduction

As a professional teacher, one of the most common questions that I get asked is about finding the least common multiple (LCM) of two or more numbers. In this article, we will focus on finding the LCM of 9 and 7, and I will explain the concept of LCM and provide step-by-step solutions to help you understand the process.

What is the Least Common Multiple?

The Least Common Multiple is the smallest multiple that two or more numbers have in common. It is the smallest number that is divisible by both numbers without a remainder. For example, the LCM of 3 and 6 is 6, because 6 is the smallest number that is a multiple of both 3 and 6.

How to Find the LCM of 9 and 7?

To find the LCM of 9 and 7, we need to find the multiples of each number and then identify the smallest multiple that they have in common. Let's start with the multiples of 9: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, 108, 117, 126, 135, 144, 153, 162, 171, 180, 189, 198, 207, 216, 225, 234, 243, 252, 261, 270, 279, 288, 297, 306, 315, 324, 333, 342, 351, 360, 369, 378, 387, 396, 405, 414, 423, 432, 441, 450 Now, let's list the multiples of 7: 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98, 105, 112, 119, 126, 133, 140, 147, 154, 161, 168, 175, 182, 189, 196, 203, 210, 217, 224, 231, 238, 245, 252, 259, 266, 273, 280, 287, 294, 301, 308, 315, 322, 329, 336, 343, 350

Identifying the Common Multiples

Now, we need to identify the common multiples of 9 and 7. Looking at the list above, we can see that the smallest multiple that they have in common is 63. Therefore, the LCM of 9 and 7 is 63.

Alternative Method

Another method to find the LCM of 9 and 7 is to use the prime factorization method. To do this, we need to find the prime factors of each number and then multiply the highest powers of each prime factor together. Let's start with 9: 9 = 3 x 3 Now, let's find the prime factors of 7: 7 = 7 Next, we need to multiply the highest powers of each prime factor together: LCM = 3 x 3 x 7 = 63

Conclusion

In conclusion, the LCM of 9 and 7 is 63. We can find the LCM by listing the multiples of each number and identifying the smallest multiple that they have in common, or by using the prime factorization method. I hope this article has helped you understand the concept of LCM and how to find it.