Understanding The Least Common Multiple Of 4 And 12

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Introduction

The concept of finding the least common multiple (LCM) of two or more numbers is an essential skill in mathematics. It is a crucial component in solving many mathematical problems. In this article, we will explore what the LCM of 4 and 12 is, and how to find it.

What is the Least Common Multiple?

The least common multiple is the smallest number that is a multiple of two or more given numbers. In simpler terms, it is the smallest number that can be divided by all of the given numbers without leaving any remainder. For example, the LCM of 2 and 3 is 6 because 6 is the smallest number that is divisible by both 2 and 3.

Finding the LCM of 4 and 12

To find the LCM of 4 and 12, we need to list down the multiples of both numbers until we find the smallest number that is common to both lists. The multiples of 4 are 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96, 100, 104, 108, 112, 116, 120, and so on. The multiples of 12 are 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, and so on.

Listing the Multiples of 4

To list the multiples of 4, we multiply 4 by each whole number. The first few multiples of 4 are:

4 x 1 = 4
4 x 2 = 8
4 x 3 = 12

Listing the Multiples of 12

To list the multiples of 12, we multiply 12 by each whole number. The first few multiples of 12 are:

12 x 1 = 12
12 x 2 = 24
12 x 3 = 36

Finding the Common Multiples

From the above lists, we can see that the common multiples of 4 and 12 are 12, 24, 36, 48, 60, 72, 84, 96, 108, and 120. The least common multiple is the smallest number that appears on both lists. In this case, the LCM of 4 and 12 is 12.

Conclusion

In conclusion, the LCM of 4 and 12 is 12. Finding the LCM of two or more numbers involves listing down the multiples of each number until we find the smallest number that appears on all lists. The LCM is a crucial concept in mathematics that is used in many different applications, including fractions, ratios, and proportions.