# Least Common Multiple Calculator

> Find the least common multiple of up to 50 whole numbers, exactly even when it is huge, with each number’s prime factorisation shown.

Category: Mathematics · Applies to: Worldwide · Last updated: 2026-10-29
Interactive calculator: https://calculators.geekmidst.com/calculators/least-common-multiple-calculator

The least common multiple is the smallest positive number that every number in the list divides into evenly. It is the lowest common denominator for adding fractions.

Also called: LCM calculator, Lowest common multiple calculator, LCD calculator.

## Inputs
- Whole numbers (default 12, 15, 20)

## Results
- Least common multiple
- LCM as prime factors
- Greatest common factor

## Formula

```
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)
```

Where:
- GCF: greatest common factor

## Worked example
1. 12 = 2² × 3, 15 = 3 × 5, 20 = 2² × 5.
2. Take each prime at its highest power: 2², 3¹ and 5¹.
3. LCM = 4 × 3 × 5 = 60.

**Result:** 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.

## Related calculators
- [Greatest Common Factor Calculator](https://calculators.geekmidst.com/calculators/greatest-common-factor-calculator)
- [Prime Factorization Calculator](https://calculators.geekmidst.com/calculators/prime-factorization-calculator)
- [Fraction Calculator](https://calculators.geekmidst.com/calculators/fraction-calculator)
- [Common Factor Calculator](https://calculators.geekmidst.com/calculators/common-factor-calculator)

Source: GM¹X CalcVerse — https://calculators.geekmidst.com/calculators/least-common-multiple-calculator