Least Common Multiple Calculator (LCM)
Enter a list of integers to calculate their least common multiple. Enter the numbers separated by a comma.
This calculator allows you to find the least common multiple of a list of input numbers. You can calculate the least common multiple (LCM) of two or more whole numbers.
How to use the least common multiple calculator?
Step 1: Enter a list of numbers for which to find the least common multiple. Numbers must be integers and must be entered separated by a comma. For example, if you want to find the LCM of 4, 6, and 8, simply enter 4,6,8.
Step 2: Click “Calculate” to get the least common multiple of the numbers entered.
Step 3: The answer will be displayed on the right. In addition, the step-by-step solution through the prime factorization method will be displayed at the bottom of the calculator.
What is the least common multiple?
The least common multiple of two numbers is the smallest possible number which is a multiple of both numbers. For example, let’s find the least common multiple of 4 and 10. The multiples of 4 are 4, 8, 12, 16, 20, 24. The multiples of 10 are 10, 20, 30, 40. We see that the least common multiple of 4 and 10 is 20.
Is it possible to calculate the least common multiple of more than two numbers?
The least common multiple can be calculated by considering more than two numbers. You can calculate the least common multiple of several numbers by entering them into the calculator above, separated by a comma.
How to calculate the least common multiple?
We can calculate the least common multiple using several methods. Two of the most important methods are by lists of multiples and by prime factorization.
Least common multiple by lists of multiples
This method consists of writing a list of various multiples of all the numbers for which we want to find the LCM. Next, we need to determine the smallest number which is a multiple of all of our original numbers.
For example, suppose we want to find the LCM of 4, 6, and 12. The multiples of these numbers are:
- 4: 4, 8, 12, 16, 20, 24, 28, 32
- 6: 6, 12, 18, 24, 30, 36, 40.
- 12: 12, 24, 36, 48.
We can see that 12 is the smallest multiple that is common to all three numbers. Therefore, 12 is the LCM of 4, 6, and 12.
Least common multiple by prime factorization
To find the LCM using this method, we first have to write the prime factorization of each number. Prime factorization consists of writing the number as a list of prime numbers so that when multiplied, they result in the original number.
Suppose we have the numbers 12, 24 and 60. Their prime factorization is:
- 12: 2, 2, 3
- 24: 2, 2, 2, 3
- 60: 2, 2, 3, 5
Then, we write each prime number as many times as it appears. For example, 2 appears three times in 24, so we write it twice. The 3 appears once in all three numbers, so we write it once. And the 5 appears once in the 60, so we write it once.
Therefore, we have 2, 2, 2, 3, 5. If we multiply these numbers, we get the LCM. Therefore, the LCM of 12, 24, and 60 is 120.
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