Least Common Denominator Calculator
Find the least common denominator of a given set of fractions with this least common denominator calculator.
Greatest common factor12
Lowest common multiple360
Coprime?Nothey share the factor 12
Product of all51,840
GCD × LCMn/athe identity only holds for two numbers
Factors of each number
| Number | Prime factors | All divisors |
|---|---|---|
| 24 | 2^3 × 3 | 1, 2, 3, 4, 6, 8, 12, 24 |
| 36 | 2^2 × 3^2 | 1, 2, 3, 4, 6, 9, 12, 18, 36 |
| 60 | 2^2 × 3 × 5 | 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 |
The method
GCD × LCM = the product of the two numbers
Finding them by factorisation
Break each number into primes. The GCD takes the lowest power of each shared prime; the LCM takes the highest power of every prime that appears.
For 24 = 2³·3 and 36 = 2²·3²: the GCD is 2²·3 = 12 and the LCM is 2³·3² = 72. Note that 12 × 72 = 864 = 24 × 36 — that identity holds for any two numbers, though not for three or more.