Understanding The Least Common Multiple Of 8 And 4

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Introduction

As a student, you may have come across the term "least common multiple" while studying mathematics. This term refers to the smallest number that is a multiple of two or more given numbers. In this article, we will be discussing the least common multiple of 8 and 4.

Finding the Multiples of 8 and 4

To find the least common multiple of 8 and 4, we must first find the multiples of both numbers. A multiple is a product of a number and any other whole number. For example, the multiples of 8 are 8, 16, 24, 32, 40, and so on. Similarly, the multiples of 4 are 4, 8, 12, 16, 20, and so on.

Identifying Common Multiples

Once we have identified the multiples of both 8 and 4, we need to find the common multiples. These are the numbers that appear in both lists of multiples. In this case, the common multiples of 8 and 4 are 8, 16, 24, and so on.

Choosing the Least Common Multiple

Out of all the common multiples, we need to choose the smallest one. This is the least common multiple of 8 and 4. In this case, the least common multiple of 8 and 4 is 8.

Why 8 is the Least Common Multiple?

We can see that 8 is the smallest number that appears in both lists of multiples. It is a multiple of 4 because 4 multiplied by 2 equals 8. Similarly, it is a multiple of 8 because 8 multiplied by 1 equals 8. Therefore, 8 is the least common multiple of 8 and 4.

Importance of Finding the Least Common Multiple

Finding the least common multiple is important in many mathematical applications. For example, it is useful when adding or subtracting fractions with different denominators. In such cases, we need to find the least common multiple of the denominators to simplify the fractions.

Using Prime Factorization to Find the Least Common Multiple

Another way to find the least common multiple is by using prime factorization. This involves breaking down each number into its prime factors and then multiplying the highest powers of each prime factor together. For example, the prime factorization of 8 is 2 x 2 x 2 and the prime factorization of 4 is 2 x 2. Therefore, the least common multiple of 8 and 4 is 2 x 2 x 2, which equals 8.

Conclusion

In conclusion, the least common multiple of 8 and 4 is 8. This is the smallest number that is a multiple of both 8 and 4. Finding the least common multiple is important in many mathematical applications and can be done by identifying the common multiples or using prime factorization.