Least Common Multiple Calculator
Enter whole positive numbers separated by white spaces or commas
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Least Common Multiple
The least common multiple (LCM) of two or more numbers is the smallest number that is a multiple of each number. The least common multiple is sometimes also called the least common factor (LCF), the lowest common divisor (LCD) or other variants thereof.
Example
What is the least common multiple of 3, 5 and 6?
Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, ...
Multiples of 5: 5, 10, 15, 20, 25, 30, 25, ...
Multiples of 6: 6, 12, 18, 24, 30, 36, ....
The first number that the list has in common is the least common multiple. This is the number 30.
Calculation method: prime factorization
There are multiple ways for calculating the least common factor. This calculator uses the prime factorization method and works as follows:
1. Break each number down into its prime factors1.
2. Find for each unique prime number the maximum number of times it occurs consecutively in some composed prime factors list.
3. Raise each unique prime number to the power of its maximum occurrences and multiply them.
Example; find the least common multiple for the numbers 12, 15 and 27
Step 1. Break each number down into its prime factors.
Prime factors of 12: 2 x 2 x 3
Prime factors of 15: 3 x 5
Prime factors of 27: 3 x 3 x 3
Step 2. Find for each prime number its maximum consecutive occurrences.
The number 2 occurs at most 2 times consecutively in the prime factor list of 12
The number 3 occurs at most 3 times consecutively in the prime factor list of 27
The number 5 occurs at most 1 time consecutively in the prime factor list of 15
Step 3. Raise each prime number to the power of its maximum occurrences and multiply them.
22 x 33 x 51 = 540
The least common multiple of 12, 15 and 27 is 540.
1The prime factors of a number are the prime numbers that multiply together to give the original number. Each prime factor may appear more than once if it is used multiple times in the multiplication. For example, the number 12 has two prime factors: 2 and 3 and can be obtained by multiplying 2 x 2 x 3.