The largest shared factor and the smallest shared multiple
Find the GCD and LCM of two or more numbers at once. Used for simplifying fractions, scheduling repeats and splitting things evenly.
These two ideas are opposites that travel together. The GCD is the biggest number dividing all of yours; the LCM is the smallest number all of yours divide into.
The GCD is how fractions get simplified. The LCM is how you work out when two repeating events coincide — buses at 12-minute and 18-minute intervals meet every 36 minutes.
The greatest common divisor of every number you enter The least common multiple of the same set Support for more than two numbers at a time Works with positive whole numbers; decimals are truncated. Numbers whose GCD is 1 are coprime — they share no factor beyond 1. What is the GCD used for in practice? Simplifying fractions, mostly. To reduce 12/18 you divide both by their GCD of 6, giving 2/3 in one step.
When would I need an LCM? Any repeating-cycle problem. Adding fractions needs a common denominator, and shift patterns or timetables that repeat every 4 and 6 days realign every 12.
What does coprime mean? Two numbers share no common factor except 1, so their GCD is 1. 8 and 15 are coprime despite neither being prime.
Is GCD × LCM related to the numbers themselves? For exactly two numbers, yes: multiply the GCD by the LCM and you get the product of the pair. With three or more it no longer holds.
Worked example Three numbers at once
Input: 12, 18, 24
Output: GCD 6 · LCM 72
Note: Six divides all three; 72 is the first number all three divide into. Note the LCM is not simply the product — that would be 5184.
