Question:What is the least common multiple of 10, 11, and 5? Show
Least Common Multiple When One Number Is a Multiple of Another:Although we will go through the whole process of the prime factorization method, our given number set is interesting because 5 is a factor of 10. We can technically just find the least common multiple of 10 and 11 because all multiples of 10 will also be multiples of 5. Answer and Explanation: 1The least common multiple of 10, 11, and 5 is 110. To find our answer, we will use the prime factorization method. To start, we break our numbers... See full answer below. Learn more about this topic:How to Find the Least Common Multiple from 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. Related to this QuestionExplore our homework questions and answers libraryWhat is the Least Common Multiple (LCM) of 10 and 5? Here we will show you step-by-step how to find the Least Common Multiple of 10 and 5. Step 1) First we find and list the prime factors of 10 and 5 (Prime Factorization): Prime Factors of 10: Prime Factors of 5: 2, 5 Step 3) Finally, we multiply the prime numbers from Step 2 together. 2 x 5 = 10 That's it. The Least Common Multiple (LCM) of 10 and 5 is 10. Least Common Multiple Calculator Least Common Multiple (LCM) of 10 and 6 Copyright | Privacy Policy | Disclaimer | Contact Calculator UseThe Least Common Multiple (LCM) is also referred to as the Lowest Common Multiple (LCM) and Least Common Divisor (LCD). For two integers a and b, denoted LCM(a,b), the LCM is the smallest positive integer that is evenly divisible by both a and b. For example, LCM(2,3) = 6 and LCM(6,10) = 30. The LCM of two or more numbers is the smallest number that is evenly divisible by all numbers in the set. Least Common Multiple CalculatorFind the LCM of a set of numbers with this calculator which also shows the steps and how to do the work. Input the numbers you want to find the LCM for. You can use commas or spaces to separate your numbers. But do not use commas within your numbers. For example, enter 2500, 1000 and not 2,500, 1,000. How to Find the Least Common Multiple LCMThis LCM calculator with steps finds the LCM and shows the work using 6 different methods:
How to Find LCM by Listing Multiples
Example: LCM(6,7,21)
How to find LCM by Prime Factorization
The LCM(a,b) is calculated by finding the prime factorization of both a and b. Use the same process for the LCM of more than 2 numbers. For example, for LCM(12,30) we find:
For example, for LCM(24,300) we find:
How to find LCM by Prime Factorization using Exponents
Example: LCM(12,18,30)
Example: LCM(24,300)
How to Find LCM Using the Cake Method (Ladder Method)The cake method uses division to find the LCM of a set of numbers. People use the cake or ladder method as the fastest and easiest way to find the LCM because it is simple division. The cake method is the same as the ladder method, the box method, the factor box method and the grid method of shortcuts to find the LCM. The boxes and grids might look a little different, but they all use division by primes to find LCM. Find the LCM(10, 12, 15, 75)
How to Find the LCM Using the Division MethodFind the LCM(10, 18, 25)
How to Find LCM by GCFThe formula to find the LCM using the Greatest Common Factor GCF of a set of numbers is: LCM(a,b) = (a×b)/GCF(a,b) Example: Find LCM(6,10)
A factor is a number that results when you can evenly divide one number by another. In this sense, a factor is also known as a divisor. The greatest common factor of two or more numbers is the largest number shared by all the factors. The greatest common factor GCF is the same as:
How to Find the LCM Using Venn DiagramsVenn diagrams are drawn as overlapping circles. They are used to show common elements, or intersections, between 2 or more objects. In using Venn diagrams to find the LCM, prime factors of each number, we call the groups, are distributed among overlapping circles to show the intersections of the groups. Once the Venn diagram is completed you can find the LCM by finding the union of the elements shown in the diagram groups and multiplying them together. How to Find LCM of Decimal Numbers
Properties of LCMThe LCM is associative:LCM(a, b) = LCM(b, a) The LCM is commutative:LCM(a, b, c) = LCM(LCM(a, b), c) = LCM(a, LCM(b, c)) The LCM is distributive:LCM(da, db, dc) = dLCM(a, b, c) The LCM is related to the greatest common factor (GCF):LCM(a,b) = a × b / GCF(a,b) and GCF(a,b) = a × b / LCM(a,b) References[1] Zwillinger, D. (Ed.). CRC Standard Mathematical Tables and Formulae, 31st Edition, New York, NY: CRC Press, 2003 p. 101. [2] Weisstein, Eric W. Least Common Multiple. From MathWorld--A Wolfram Web Resource. What is the common multiple of 10 and 5?The multiples of 5 include 5, 10, 15, 20, 25, 30, 35, 40,…. The multiples of 10 include 10, 20, 30, 40, 50, 60,…. Thus, the common multiples of 5 and 10 are 10, 20, 30, 40,…. That means all the multiples of 10 will be the common multiples for 5 and 10.
What is the GCF and LCM of 5 and 10?GCF of 5 and 10 Examples
Therefore, the greatest common factor of 5 and 10 is 5. Example 2: The product of two numbers is 50. If their GCF is 5, what is their LCM? Therefore, the LCM is 10.
|