DIY Cost Tools
LCM Calculator
MATH CALCULATOR
Find the least common multiple (LCM) of two or more positive integers. Separate numbers with commas, spaces, or line breaks.
How it works
The calculator combines the numbers one at a time using their greatest common factor, which avoids searching through every multiple.
Formula
LCM(a, b) = |a × b| ÷ GCF(a, b).
Example
The LCM of 12, 18, and 30 is 180. It is the smallest positive number divisible by all three.
Common uses
- Finding a common denominator for fractions
- Matching repeating schedules or cycles
- Working with ratios, gears, and grouped quantities
Frequently asked questions
Is the LCM always the product?
No. It equals the product only when the numbers share no factor greater than 1.
Can I enter more than two numbers?
Yes. Add as many positive integers as needed, separated by commas or spaces.
Using the least common multiple
The least common multiple is the smallest positive number divisible by every selected integer. It helps combine fraction denominators and identify when repeating schedules will align. For example, events repeating every 6 and 8 days coincide every 24 days.
A useful check for two positive integers is LCM(a,b) = |a × b| ÷ GCF(a,b). Reduce by the GCF before multiplying when numbers are large to avoid unnecessary intermediate values. Most practical uses assume nonzero whole numbers; if an input is zero, many conventions define the LCM as zero. For schedules, verify that each interval begins from the same starting time—different start offsets can change the next actual coincidence even when the interval LCM is correct.
Review notes
The method uses the Euclidean algorithm for the GCF and the standard LCM identity. Last reviewed September 30, 2026.