The Least Common Multiple Of 10 And 12

LCM of 10 and 12 How to Find LCM of 10, 12? from www.cuemath.com

Introduction

In mathematics, the least common multiple (LCM) of two or more numbers is the smallest number that can be evenly divided by all of them. In this article, we will be discussing the LCM of 10 and 12.

Factors of 10 and 12

To find the LCM of 10 and 12, we first need to determine the factors of both numbers. The factors of 10 are 1, 2, 5, and 10. The factors of 12 are 1, 2, 3, 4, 6, and 12.

Method 1: Listing Multiples

One way to find the LCM of 10 and 12 is to list their multiples until we find the smallest number that is divisible by both numbers. The multiples of 10 are 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, and so on. The multiples of 12 are 12, 24, 36, 48, 60, 72, 84, 96, 108, and so on. From this list, we can see that the smallest number that is divisible by both 10 and 12 is 60.

Method 2: Prime Factorization

Another method to find the LCM of 10 and 12 is to use prime factorization. We can write 10 as 2 x 5 and 12 as 2 x 2 x 3. Then, we take the highest power of each prime factor and multiply them together. In this case, the highest power of 2 is 2^2, the highest power of 3 is 3^1, and the highest power of 5 is 5^1. Multiplying these together gives us 2^2 x 3^1 x 5^1 = 60, which is the LCM of 10 and 12.

Conclusion

In conclusion, the LCM of 10 and 12 is 60. We can find it by listing their multiples or using prime factorization. The LCM is an important concept in mathematics, especially in fractions and algebra.