How it works
Calculate the Least Common Multiple (LCM) of two or more numbers.
Input query strings and outputs
Use an input name in this page’s URL as ?name=value, and join additional inputs with &. Portable shared links may instead use the compact ?ac= state parameter.
Input query strings
1-
?numbers=Enter numbers (comma separated)Text · Optional · Default: 12, 18, 24
Outputs
1-
resultResultText · Primary output
result contains the calculator’s complete rendered result area, including its visible result cards, tables, charts, and messages.
Find the smallest shared multiple of multiple numbers
Description
The Least Common Multiple (LCM) Calculator determines the smallest positive integer that is a multiple of every number in a given set. This is most commonly used in mathematics for finding a Least Common Denominator when adding or subtracting fractions, but it is also essential in fields like physics and scheduling to find when repeating cycles will synchronize.
Inputs
- Numbers: A list of two or more integers separated by commas or spaces (e.g.,
12, 18, 24).
Outputs
- LCM: The smallest value that is divisible by all numbers in your list.
Chart
- N/A: This tool provides a direct numeric result.
“Good to Know”
- Fractions: To add 1/12 and 1/18, you find the LCM of 12 and 18 (which is 36). This becomes your common denominator (3/36 + 2/36 = 5/36).
- The GCD Relationship: For two numbers $a$ and $b$, the LCM can be found using the formula: $LCM(a, b) = |a \cdot b| / GCF(a, b)$.
- Cycles: If one light flashes every 4 seconds and another every 6 seconds, they will flash together every 12 seconds (the LCM of 4 and 6).
Examples
Example 1: Common Denominator
- Input:
4, 6 - Output: 12
Example 2: Three Numbers
- Input:
12, 18, 24 - Output: 72
Example 3: Prime Numbers
- Input:
3, 5, 7 - Output: 105 (When numbers are prime, the LCM is just their product)