What Is The Lcm Of 8 And 10?

LCM of 8 and 10 How to Find LCM of 8, 10? from www.cuemath.com

Introduction

In mathematics, LCM stands for Least Common Multiple. It is the smallest positive integer that is divisible by both the numbers. In this article, we will discuss how to find the LCM of 8 and 10.

Method 1: Listing Multiples

One way to find the LCM of 8 and 10 is by listing their multiples. Multiples of 8 are 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104, 112, 120, 128, 136, 144, 152, 160, 168, 176, 184, 192, 200, 208, 216, 224, 232, 240, 248, 256, 264, 272, 280, 288, 296, 304, 312, 320, 328, 336, 344, 352, 360, 368, 376, 384, 392, 400, 408, 416, 424, 432, 440, 448, 456, 464, 472, 480, 488, 496, and so on. Similarly, multiples of 10 are 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, and so on.

Step 1:

We need to find the common multiples of both 8 and 10. From the above multiples, we can see that 40, 80, 120, 160, 200, 240, 280, 320, 360, and so on are the common multiples of 8 and 10.

Step 2:

Out of the common multiples, we need to find the smallest one. The smallest common multiple of 8 and 10 is 40. Therefore, the LCM of 8 and 10 is 40.

Method 2: Prime Factorization

Another way to find the LCM of 8 and 10 is by using prime factorization.

Step 1:

We need to find the prime factors of both 8 and 10. The prime factors of 8 are 2 x 2 x 2, and the prime factors of 10 are 2 x 5.

Step 2:

We need to write the prime factors in exponential form. The prime factors of 8 can be written as 2^3. The prime factors of 10 can be written as 2 x 5^1.

Step 3:

We need to take the highest power of each prime factor. In this case, we need to take the highest power of 2 and 5. The highest power of 2 is 2^3. The highest power of 5 is 5^1.

Step 4:

We need to multiply the highest power of each prime factor. 2^3 x 5^1 = 40. Therefore, the LCM of 8 and 10 is 40.

Conclusion

In conclusion, the LCM of 8 and 10 can be found using different methods. One way is by listing their multiples and finding the smallest common multiple. Another way is by using prime factorization and taking the highest power of each prime factor. Both methods give the same answer, which is 40.