Least Common Multiple Calculator
Please provide numbers separated by a comma "," and click the "Calculate" button to find the LCM.
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.
|EX:|| Find LCM(18, 26)|
18: 18, 36, 54, 72, 90, 108, 126, 144, 162, 180, 198, 216, 234
26: 52, 78, 104, 130, 156, 182, 208, 234
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:
|EX:|| Find LCM(21, 14, 38)|
21 = 3 × 7
14 = 2 × 7
38 = 2 × 19
The LCM is therefore:
3 × 7 × 2 × 19 = 798
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:
|EX:|| Find LCM(21, 14, 38)|
GCF(14, 38) = 2
GCF(266, 21) = 7
LCM(21, 14, 38) = 798
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.
What is the Least Common Multiple (LCM) of 19 and 16?
If you are searching to find out what the lowest common multiple of 19 and 16 is then you probably figured out you are in the right place! That's exactly what this quick guide is all about. We'll walk you through how to calculate the least common multiple for any numbers you need to check. Keep reading!
First off, if you're in a rush, here's the answer to the question "what is the LCM of 19 and 16?":
LCM(19, 16) = 304
What is the Least Common Multiple?
In simple terms, the LCM is the smallest possible whole number (an integer) that divides evenly into all of the numbers in the set. It's also sometimes called the least common divisor, or LCD.
There are a number of different ways to calculate the GCF of a set of numbers depending how many numbers you have and how large they are.
For smaller numbers you can simply look at the factors or multiples for each number and find the least common multiple of them.
For 19 and 16 those factors look like this:
- Factors for 19: 1, 2, 4, 8, 16, 19, 38, 76, 152, and 304
- Factors for 16: 1, 2, 4, 8, 16, 19, 38, 76, 152, and 304
As you can see when you list out the factors of each number, 304 is the greatest number that 19 and 16 divides into.
As the numbers get larger, or you want to compare multiple numbers at the same time to find the GCF, you can see how listing out all of the factors would become too much. To fix this, you can use prime factors.
List out all of the prime factors for each number:
- Prime Factors for 19: 19
- Prime Factors for 16: 2, 2, 2, and 2
Now that we have the list of prime factors, we need to list out all of the prime factors as often as they occur for each given number and then multiply them together. In our example, this becomes:
LCM = 19 x 2 = 38
Other Ways to Calculate LCM
There are a number of other ways in which you can calculate the least common multiple of numbers, including:
- Prime factorization using exponents
- The cake/ladder method
- The division method
- Using the greatest common factor (GCF)
For the purposes of this tutorial, using factors or prime factors should help you to calculate the answer easily. If you really want to brush up on your math, you can research the other methods and become a full blown LCM expert.
Hopefully you've learned a little math today (but not too much!) and understand how to calculate the LCM of numbers. The next challenge is to pick a couple of new numbers yourself and try to work it out using the above methods.
Not feeling like doing the hard work? No worries! Head back to our LCM calculator instead and let our tool do the hard work for you :)
Cite, Link, or Reference This Page
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<a href="https://visualfractions.com/calculator/least-common-multiple/lcm-of-19-and-16/">Least Common Multiple of 19 and 16</a>
"Least Common Multiple of 19 and 16". VisualFractions.com. Accessed on October 22, 2021. https://visualfractions.com/calculator/least-common-multiple/lcm-of-19-and-16/.
"Least Common Multiple of 19 and 16". VisualFractions.com, https://visualfractions.com/calculator/least-common-multiple/lcm-of-19-and-16/. Accessed 22 October, 2021.
Least Common Multiple of 19 and 16. VisualFractions.com. Retrieved from https://visualfractions.com/calculator/least-common-multiple/lcm-of-19-and-16/.
Random List of LCM Examples
Here is a list of random least common multiple problems for you to enjoy:
Popular List of LCM Examples
Here are some of the mostly commonly searched for LCM problems for you to enjoy:
LCM of 19 and 38
FAQs on LCM of 19 and 38
What is the LCM of 19 and 38?
The LCM of 19 and 38 is 38. To find the least common multiple (LCM) of 19 and 38, we need to find the multiples of 19 and 38 (multiples of 19 = 19, 38, 57, 76; multiples of 38 = 38, 76, 114, 152) and choose the smallest multiple that is exactly divisible by 19 and 38, i.e., 38.
How to Find the LCM of 19 and 38 by Prime Factorization?
To find the LCM of 19 and 38 using prime factorization, we will find the prime factors, (19 = 19) and (38 = 2 × 19). LCM of 19 and 38 is the product of prime factors raised to their respective highest exponent among the numbers 19 and 38.
⇒ LCM of 19, 38 = 21 × 191 = 38.
Which of the following is the LCM of 19 and 38? 5, 18, 11, 38
The value of LCM of 19, 38 is the smallest common multiple of 19 and 38. The number satisfying the given condition is 38.
What are the Methods to Find LCM of 19 and 38?
The commonly used methods to find the LCM of 19 and 38 are:
- Division Method
- Prime Factorization Method
- Listing Multiples
If the LCM of 38 and 19 is 38, Find its GCF.
LCM(38, 19) × GCF(38, 19) = 38 × 19
Since the LCM of 38 and 19 = 38
⇒ 38 × GCF(38, 19) = 722
Therefore, the GCF = 722/38 = 19.
What is the Least Common Multiple (LCM) of 19 and 3? Here we will show you step-by-step how to find the Least Common Multiple of 19 and 3.
Step 1)First we find and list the prime factors of 19 and 3 (Prime Factorization):
Prime Factors of 19:
Prime Factors of 3:
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:
Step 3)Finally, we multiply the prime numbers from Step 2 together.
3 x 19 = 57
That's it. The Least Common Multiple (LCM) of 19 and 3 is 57.
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 19 and 4
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LCM Calculator - Least Common Multiple
The LCM calculator will determine the least common multiple of two to fifteen numbers for you - no need to fret! This calculation is essential when adding or subtracting fractions with different denominators. The following text will explain what is LCM, show how to find the least common multiple and show how to use the least common multiple calculator.
What is LCM?
The LCM is the least common multiple or lowest common multiple between two or more numbers. We can find the least common multiple by breaking down each number into its prime factors. This can be accomplished by hand or by using the factor calculator or prime factorization calculator. The method for finding the LCM, along with an example illustrating the method, will be seen in the next section.
How to find the Least Common Multiple
Take each number and find its prime factors. Knowing various divisibility rules helps assist in this process.
- Any even number is divisible by .
- Any numbers whose sum of the digits is divisible by , is also divisible by
- A number is divisible by if the last two digits of the number form a number that is divisible by
- All numbers ending in or are divisible by .
- The number is divisible by if it is divisible by both and .
- A number is divisible by if the last three digits of the number form a number that is divisible by .
- A number whose digits sum to a number divisible by is also divisible by .
- Any number ending in is divisible by .
Once the numbers are broken down to their prime factors, multiply the highest power of each factor to get the LCM.
Least Common Multiple calculator
We are going to show how to find the LCM of , and . First we'll get the factors of each number. These are: ,, . Gather all the factors, so we have . Next multiply the highest power of each of these factors. That gives us . The LCM calculator can be used to check your answer or simply perform this calculation for you.
A Related Concept: The GCF
Just as you need prime factorization to get the LCM, it's equally important to find the GCF, which is the greatest common factor. To find the GCF, take the product of all the common factors of each number. For example, the GCF of and is since the only factor in common between the two numbers is . The GCF calculatoris a handy tool to calculate this.
Note that the LCM of two integers is the smallest positive integer the is divisible by both the integers. This is only true if both the integers are not zero. The LCM calculator will display a value of zero in such a case that one or more of the numbers is zero.
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