What is the least common multiple of 11 and 8

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What is the Least Common Multiple (LCM)?

In mathematics, the least common multiple, also known as the lowest common multiple of two (or more) integers a and b, is the smallest positive integer that is divisible by both. It is commonly denoted as LCM(a, b).

Brute Force Method

There are multiple ways to find a least common multiple. The most basic is simply using a "brute force" method that lists out each integer's multiples.

As can be seen, this method can be fairly tedious, and is far from ideal.

Prime Factorization Method

A more systematic way to find the LCM of some given integers is to use prime factorization. Prime factorization involves breaking down each of the numbers being compared into its product of prime numbers. The LCM is then determined by multiplying the highest power of each prime number together. Note that computing the LCM this way, while more efficient than using the "brute force" method, is still limited to smaller numbers. Refer to the example below for clarification on how to use prime factorization to determine the LCM:

Greatest Common Divisor Method

A third viable method for finding the LCM of some given integers is using the greatest common divisor. This is also frequently referred to as the greatest common factor (GCF), among other names. Refer to the link for details on how to determine the greatest common divisor. Given LCM(a, b), the procedure for finding the LCM using GCF is to divide the product of the numbers a and b by their GCF, i.e. (a × b)/GCF(a,b). When trying to determine the LCM of more than two numbers, for example LCM(a, b, c) find the LCM of a and b where the result will be q. Then find the LCM of c and q. The result will be the LCM of all three numbers. Using the previous example:

Note that it is not important which LCM is calculated first as long as all the numbers are used, and the method is followed accurately. Depending on the particular situation, each method has its own merits, and the user can decide which method to pursue at their own discretion.

Question:

What is the least common multiple of 8, 9, and 11?

Prime Factorization Method:

To find the least common multiple of three numbers, we need to use the prime factorization method to simplify the process into three steps. The first step is to create a prime factorization for each given number. The second step compares the factorization lists to identify the most times each prime number is repeated in a factorization. The last step is to extract only the groups of a prime number that are repeated the most, then multiply those groups together. Once we multiply, the product will be our answer.

Answer and Explanation: 1

The least common multiple of 8, 9, and 11 is 792.

To find the least common multiple of 8, 9, and 11, we start by breaking down each of our given...

See full answer below.

Learn more about this topic:

How to Find the Least Common Multiple

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Chapter 1 / Lesson 4

Learn how to find the least common multiple of two or more numbers. Discover the least common multiple definition, methods for finding them, and see examples.

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What is the Least Common Multiple (LCM) of 8 and 11? Here we will show you step-by-step how to find the Least Common Multiple of 8 and 11.

Step 1) First we find and list the prime factors of 8 and 11 (Prime Factorization):

Prime Factors of 8:
2, 2, 2

Prime Factors of 11:
11

2, 2, 2, 11 Step 3) Finally, we multiply the prime numbers from Step 2 together.

2 x 2 x 2 x 11 = 88 That's it. The Least Common Multiple (LCM) of 8 and 11 is 88.

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