LCM & GCD Calculator
Calculate the Least Common Multiple and Greatest Common Divisor of multiple numbers.
Enter Numbers
Results
Enter numbers and click Calculate to see the results
LCM & GCD Explained
Least Common Multiple (LCM)
The smallest positive number that is divisible by all the given numbers without a remainder.
For numbers a and b, LCM is the smallest positive number that is a multiple of both a and b.
Example: LCM of 4 and 6 is 12, as 12 is the smallest number divisible by both 4 and 6.
Greatest Common Divisor (GCD)
The largest positive integer that divides all the given numbers without a remainder.
For numbers a and b, GCD is the largest positive integer that divides both a and b without a remainder.
Example: GCD of 12 and 18 is 6, as 6 is the largest number that divides both 12 and 18.
Calculation Methods
This calculator uses efficient algorithms to find LCM and GCD:
- Euclidean algorithm for GCD
- LCM calculation using the formula: LCM(a,b) = (a × b) / GCD(a,b)
- For multiple numbers, calculations are done pairwise
Applications
LCM and GCD have many practical applications:
- Fractions: Finding common denominators (LCM)
- Simplifying fractions (GCD)
- Cryptography and number theory
- Scheduling and timing problems
Tips & Notes
- Enter positive integers only. Decimal numbers will be truncated to integers.
- You can calculate LCM and GCD for up to 10 numbers at once.
- The GCD of any number and 0 is the number itself.
- The LCM of any number and 0 is 0.
- For very large numbers, calculations might take longer to process.
- The calculator can handle numbers up to 10^15 (one quadrillion).