What Is The Least Common Multiple Of 9 And 10?

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Introduction

In mathematics, we often come across a situation where we need to find the least common multiple (LCM) of two or more numbers. LCM is the smallest number that is divisible by all the given numbers without a remainder. In this article, we will discuss how to find the LCM of 9 and 10.

Method 1: Prime Factorization

One of the most common methods to find the LCM of two numbers is by prime factorization. To use this method, we need to find the prime factors of each number and then multiply the highest power of each prime factor. Let's find the prime factors of 9 and 10. 9 = 3 x 3 10 = 2 x 5 Now, we need to take the highest power of each prime factor. In this case, we have only two prime factors, which are 2 and 3. The highest power of 2 is 1, and the highest power of 3 is 2. Therefore, the LCM of 9 and 10 is 2 x 3 x 3 = 18.

Method 2: Listing Multiples

Another way to find the LCM of two numbers is by listing their multiples. We can start by listing the multiples of 9 and 10 and find the smallest multiple that is common to both lists. Let's list the multiples of 9 and 10. 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, 459, 468, 477, 486, 495, 504, 513, 522, 531, 540, 549, 558, 567, 576, 585, 594, 603, 612, 621, 630, 639, 648, 657, 666, 675, 684, 693, 702, 711, 720 Multiples of 10: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200, 210, 220, 230, 240, 250, 260, 270, 280, 290, 300, 310, 320, 330, 340, 350, 360, 370, 380, 390, 400, 410, 420, 430, 440, 450, 460, 470, 480, 490, 500, 510, 520, 530, 540, 550, 560, 570, 580, 590, 600, 610, 620, 630, 640, 650, 660, 670, 680, 690, 700, 710, 720 From the above lists, we can see that the smallest multiple that is common to both lists is 90. Therefore, the LCM of 9 and 10 is 90.

Conclusion

In conclusion, we have discussed two methods to find the LCM of 9 and 10. The first method involves prime factorization, where we find the prime factors of each number and multiply the highest power of each prime factor. The second method involves listing multiples, where we list the multiples of each number and find the smallest multiple that is common to both lists. Both methods give the same answer, which is 90.