How to use this calculator
- Enter or choose whole numbers.
- The least common multiple updates as you type. Use Copy result or Share to keep it.
Method
LCM = product of each prime raised to its highest power in any of the numbers; for two numbers, LCM(a, b) = a × b ÷ GCF(a, b)
- GCF
- greatest common factor
Worked example
- 12 = 2² × 3, 15 = 3 × 5, 20 = 2² × 5.
- Take each prime at its highest power: 2², 3¹ and 5¹.
- LCM = 4 × 3 × 5 = 60.
The least common multiple of 12, 15 and 20 is 60.
What the result means
To add 1/12 + 1/15 + 1/20, rewrite each fraction over 60. In scheduling, events that repeat every 12, 15 and 20 days coincide every 60 days.
Assumptions and limits
- Positive whole numbers up to 1,000,000,000,000.
Questions
What is the difference between LCM and GCF?
The LCM is the smallest number all of them divide into; the GCF is the largest number that divides all of them. For two numbers, LCM × GCF = a × b.
Is the LCM ever smaller than the largest number?
No. It is at least as large as the largest number, and equals it when the largest is a multiple of all the others.