Learn how to find the Least Common Multiple (LCM) of 12 and 8 with this comprehensive guide. Discover what factors are and how to determine common factors.
Introduction
When working with numbers, it’s essential to understand the concept of LCM or Least Common Multiple. LCM is the smallest number that is a multiple of two or more numbers. In this article, we will discuss what LCM is and how to find the LCM of 12 and 8, two common numbers used in arithmetic.
Factors of 12 and 8
Before we can determine the LCM of 12 and 8, we need to understand what factors are. Factors are the numbers that can be multiplied together to obtain a given number. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12. Similarly, the factors of 8 are 1, 2, 4, and 8.
To find the factors of a number, we need to divide the number by all the numbers that come before it. For example, to find the factors of 12, we divide 12 by 1, 2, 3, 4, 6, and 12. This gives us the factors of 12. Similarly, to find the factors of 8, we divide 8 by 1, 2, 4, and 8. This gives us the factors of 8.
Knowing the factors of 12 and 8 is crucial in finding their common factors, which is the next step in determining their LCM.
Common factors
The next step in finding the LCM of 12 and 8 is to identify their common factors. Common factors are the factors that are common to two or more numbers. In this case, the common factors of 12 and 8 are 1, 2, and 4. These numbers can be found by comparing the factors of 12 and 8. We can see that both 12 and 8 have the factors 1, 2, and 4.
Greatest common factor
The greatest common factor (GCF) is the largest factor that is common to two or more numbers. In this case, the GCF of 12 and 8 is 4. We can determine this by looking at the common factors of 12 and 8, which are 1, 2, and 4. The largest of these common factors is 4, so it is the greatest common factor of 12 and 8.
The GCF is an important factor in finding the LCM of two numbers. To find the LCM of 12 and 8, we need to multiply their GCF by any remaining factors that are not common to both numbers. In this case, the remaining factor of 3 for 12 and the remaining factor of 2 for 8 are not common, so we need to multiply the GCF of 4 by 3 and 2.
4 x 3 = 12
4 x 2 = 8
Therefore, the LCM of 12 and 8 is 24. The LCM is the smallest number that is a multiple of both 12 and 8. In this case, 24 is divisible by both 12 and 8.
Understanding LCM and GCF is essential in solving many math problems. By following the steps outlined above, we can easily find the LCM of any two numbers.
Least common multiple
Now that we know the factors of 12 and 8, we can find their least common multiple (LCM). The LCM is the smallest number that is a multiple of both 12 and 8. To find the LCM of 12 and 8, we need to list their multiples and find the smallest number that appears in both lists.
The multiples of 12 are 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, and so on. The multiples of 8 are 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, and so on. From these lists, we can see that the smallest number that appears in both lists is 24. Therefore, the LCM of 12 and 8 is 24.
Conclusion
In conclusion, the LCM is an essential concept in arithmetic that is used to find the smallest number that is a multiple of two or more numbers. To find the LCM of 12 and 8, we first need to find their factors and then determine their least common multiple. In this case, the LCM of 12 and 8 is 24. Understanding LCM is crucial in solving many arithmetic problems and is a fundamental concept in mathematics.
