Least Common Multiple Calculator
Type two or more positive whole numbers, separated by commas or spaces, and press Find LCM. The calculator returns the least common multiple, the smallest number that each of them divides. It works exactly at any size, so long numbers keep every digit. A 0, a negative number, a decimal or a word gets a message that names it.
How to use the Least Common Multiple Calculator
- Enter your numbers in the Least Common Multiple Calculator above.
- Press the Find LCM button to see the result.
- To try other numbers, change any value and press the button again.
The LCM via GCD
LCM(a, b) = (a × b) / GCD(a, b) · · · LCM of 3+ numbers: pairwise apply
For two numbers, LCM × GCD = product of the numbers. For more than two, apply pairwise: LCM(a,b,c) = LCM(LCM(a,b), c).
Worked example
LCM(12, 18): GCD is 6, so LCM = (12 × 18)/6 = 36. LCM(4, 6, 10): LCM(4,6) = 12; LCM(12,10) = 60.
Frequently asked questions
When do I use LCM in real life?
Adding fractions with different denominators (find common denominator), scheduling repeating events that coincide, gear ratios, music theory and project scheduling.
Is LCM the same as common multiple?
Common multiples are any number divisible by all given numbers. LCM is the smallest such positive number. Multiples of LCM are also common multiples (LCM × 2, LCM × 3, etc.).
What if one number is 0?
Every multiple of 0 is 0, so no positive number is a multiple of 0 and there is no least positive common multiple. The calculator asks for positive whole numbers and gives a message for a 0.