Least Common Multiple (LCM) of 9 and 8 Show  Step 1) First we find and list the prime factors of 9 and 8 (Prime Factorization): Prime Factors of 9: 3, 3 Prime Factors of 8: 2, 2, 2 Step 2) Then we look at the frequency of the prime factors as they appear in each set above. List each prime factor the greatest number of times it occurs in either sets: 2, 2, 2, 3, 3 Step 3) Finally, we multiply the prime numbers from Step 2 together. 2 x 2 x 2 x 3 x 3 = 72 That's it. The Least Common Multiple (LCM) of 9 and 8 is 72. Least Common Multiple Calculator Please enter another two or three numbers below so we can calculate the Least Common Multiple (LCM) for you: Least Common Multiple (LCM) of 9 and 9 Here is the next set of numbers we found the Least Common Multiple for. Copyright | Privacy Policy | Disclaimer | ContactAnswer Hint: To calculate the LCM of three numbers, we should first find the prime factorisation of all three numbers, and then, we can write LCM by multiplying the prime factors as many times as the maximum number of times of their occurrence in any given number. Complete step by step answer: Least Common Multiple or LCM of three numbers, a, b and c, is defined as the smallest number possible that is perfectly divisible by all three a, b and c.To use the prime factorisation method, we will first have to calculate the prime factorisation, and then list the prime factors as many times as the maximum number of times of their occurrence.Here in this question, we need to calculate the LCM of 6, 8 and 9.The prime factorisation of 6 is:\[\begin{align} & 2\left| \!{\underline {\, 6 \,}} \right. \\ & 3\left| \!{\underline {\, 3 \,}} \right. \\ & \text{ }\left| \!{\underline {\, 1 \,}} \right. \\ \end{align}\] $\therefore 6=2\times 3$ The prime factorisation of 8 is:\[\begin{align} & 2\left| \!{\underline {\, 8 \,}} \right. \\ & 2\left| \!{\underline {\, 4 \,}} \right. \\ & 2\left| \!{\underline {\, 2 \,}} \right. \\ & \text{ }\left| \!{\underline {\, 1 \,}} \right. \\ \end{align}\]$\therefore 8=2\times 2\times 2$ The prime factorisation of 9 is:\[\begin{align} & 3\left| \!{\underline {\, 9 \,}} \right. \\ & 3\left| \!{\underline {\, 3 \,}} \right. \\ & \text{ }\left| \!{\underline {\, 1 \,}} \right. \\ \end{align}\] $\therefore 9=3\times 3$Now, for the prime factor 2, we have,The number of times of occurrence of 2 in prime factorisation of 6 = 1The number of times of occurrence of 2 in prime factorisation of 8 = 3The number of times of occurrence of 2 in prime factorisation of 9 = 0So, the maximum number of times of occurrence of 2 = 3 …(i)Similarly, for the prime factor 3, we have,The number of times of occurrence of 3 in prime factorisation of 6 = 1The number of times of occurrence of 3 in prime factorisation of 8 = 0The number of times of occurrence of 3 in prime factorisation of 9 = 2So, the maximum number of times of occurrence of 3 = 2 …(ii)Now using (i) and (ii), we can say that 2 must occur thrice, and 3 must occur twice. Thus,$LCM=2\times 2\times 2\times 3\times 3$ $\Rightarrow LCM=72$Hence, the LCM of 6, 8 and 9 is 72. Note: Here, we can notice that the two numbers 8 and 9 do not have a common factor other than 1. So, the LCM of 8 and 9 will be $LCM=8\times 9=72$. We also see that 72 is divisible by 6. So, the LCM of 6, 8 and 9 will be 72. The lcm of 9 and 8 is the smallest positive integer that divides the numbers 9 and 8 without a remainder. Spelled out, it is the least common multiple of 9 and 8. Here you can find the lcm of 9 and 8, along with a total of three methods for computing it. This Least Common Multiple Calculator is Really Cool! Click To TweetIn addition, we have a calculator you should check out. Not only can it determine the lcm of 9 and 8, but also that of three or more integers including nine and eight for example. Keep reading to learn everything about the lcm (9,8) and the terms related to it.What is the LCM of 9 and 8If you just want to know what is the least common multiple of 9 and 8, it is 72. Usually, this is written as lcm(9,8) = 72The lcm of 9 and 8 can be obtained like this:
Taking the above into account you also know how to find all the common multiples of 9 and 8, not just the smallest. In the next section we show you how to calculate the lcm of nine and eight by means of two more methods. How to find the LCM of 9 and 8The least common multiple of 9 and 8 can be computed by using the greatest common factor aka gcf of 9 and 8. This is the easiest approach: lcm (9,8) = = 72Alternatively, the lcm of 9 and 8 can be found using the prime factorization of 9 and 8:
In any case, the easiest way to compute the lcm of two numbers like 9 and 8 is by using our calculator below. Note that it can also compute the lcm of more than two numbers, separated by a comma. For example, enter 9,8. Push the button only to start over. Similar searched terms on our site also include:
Use of LCM of 9 and 8What is the least common multiple of 9 and 8 used for? Answer: It is helpful for adding and subtracting fractions like 1/9 and 1/8. Just multiply the dividends and divisors by 8 and 9, respectively, such that the divisors have the value of 72, the lcm of 9 and 8. . . Properties of LCM of 9 and 8The most important properties of the lcm(9,8) are:
The associativity is particularly useful to get the lcm of three or more numbers; our calculator makes use of it. To sum up, the lcm of 9 and 8 is 72. In common notation: lcm (9,8) = 72. If you have been searching for lcm 9 and 8 or lcm 9 8 then you have come to the correct page, too. The same is the true if you typed lcm for 9 and 8 in your favorite search engine. Note that you can find the least common multiple of many integer pairs including nine / eight by using the search form in the sidebar of this page. Questions and comments related to the lcm of 9 and 8 are really appreciated. Use the form below or send us a mail to get in touch. Please hit the sharing buttons if our article about the least common multiple of 9 and 8 has been useful to you, and make sure to bookmark our site. Thanks for your visit. The full form of LCM is Least Common Multiple and also noted as Lowest Common Multiple (LCM) or Least Common Divisor (LCD). LCM is the smallest positive integer that is equally divisible by two integers a and b. It is denoted as LCM(a,b). For example, if you take integer a=8 and b=12, the LCM(a,b) i.e., LCM(8,12)=24. Use this free online LCM Calculator and provide the input numbers that are given to calculate the LCM of two integers. Give the first input in the number 1 field and then second input in the number 2 field and press on the ‘Calculate’ button which is colored in blue. Remember not to use commas within your numbers like 5,000, 7,500. Ex: LCM of 44 and 60 (or) LCM of 45 and 30 (or) LCM of 32 and 48 Here are some samples of LCM of two numbers calculations. |
What is the least common multiple of 9 and 8?
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