GCD and LCM calculator
The greatest common divisor is the largest number dividing both; the least common multiple is the smallest number both divide into. The two are linked: their product equals the product of the original numbers.
Greatest common divisor
12
- Least common multiple
- 72
Rates and thresholds
- GCD(24, 36)
- 12
- LCM(24, 36)
- 72
- Relationship
- GCD × LCM = a × b
How do I find the greatest common divisor?
The quickest route is Euclid's algorithm: divide the larger by the smaller and replace the larger with the remainder until the remainder is zero — the last non-zero remainder is the GCD. For 36 and 24: 36 ÷ 24 leaves 12, and 24 ÷ 12 leaves 0, so the GCD is 12.
What is the least common multiple for?
Most often for adding fractions: the common denominator is the least common multiple of the denominators. Adding a third and a quarter, the LCM is 12, so 4/12 + 3/12 = 7/12. The same number answers when two events on different cycles next coincide.
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