Least Common Multiple Calculator
Find the smallest positive multiple shared by two whole numbers.
Result
Least common multiple: 72 multiple
The result is the smallest positive number divisible by both inputs.
- Greatest common factor
- 6
- Multiplier for first number
- 4
- Multiplier for second number
- 3
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How to use the Least Common Multiple Calculator
- Enter two positive whole numbers.
- Read the smallest positive multiple shared by both.
- Use the multipliers to verify how each input reaches the LCM.
The first multiple the numbers share
Listing multiples works for small values, but the relationship with the GCF is faster and exact:
lcm(a,b) = |a ÷ gcd(a,b) × b|Dividing by the GCF first keeps the intermediate product smaller. The result is then divided by each input to show its whole-number multiplier.
With your numbers
- GCF(18, 24) = 6.
- LCM = first ÷ GCF × second = 72.
Quick reference
The result is the smallest positive number divisible by both inputs.
| Example | Least common multiple |
|---|---|
| 18 and 24 | 72 |
| 15 and 20 | 60 |
| 7 and 9 | 63 |
| 12 and 18 | 36 |
| 25 and 100 | 100 |
| 8 and 8 | 8 |
Common questions about the Least Common Multiple Calculator
- What is a least common multiple?
- It is the smallest positive whole number divisible by both entered numbers.
- How is LCM related to GCF?
- For positive integers, LCM equals the absolute product divided by the GCF.
- Why divide before multiplying?
- It lowers the intermediate value and reduces overflow risk while producing the same exact integer.
- How does LCM help with fractions?
- The LCM of denominators is their least common denominator for addition or subtraction.