Event synchronization
- Input
- MMC(4, 6, 10)
- Expected output
- 60
The three cycles line up again at the smallest number that is a multiple of all three, computed in two steps: LCM(4,6)=12, then LCM(12,10)=60.
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LCM of multiple numbers
LCM(a,b,c) = LCM(LCM(a,b),c): the tool applies this rule pairwise for up to 10 numbers at once, always reusing the GCD it computes internally at each step. The result is never smaller than the largest number in the list.
The three cycles line up again at the smallest number that is a multiple of all three, computed in two steps: LCM(4,6)=12, then LCM(12,10)=60.
The minimum denominator to add 1/3, 1/4 and 1/5 without simplifying afterward: any smaller denominator would leave one of the three fractions without a whole-number form.
Two machines complete a cycle every 18 and 24 seconds: they finish together again every 72 seconds, the smallest common multiple of the two intervals.
GCD (Greatest Common Divisor) is the largest positive integer that divides all numbers in the set without a remainder. It can be found with the Euclidean algorithm or by comparing prime factorizations and taking the lowest power of each shared prime. For example, GCD(12, 18) = 6.
Not directly: the equality only holds pairwise. For 3 or more numbers, the LCM has to be computed in stages, LCM(LCM(a,b),c), because the original relation depends on each prime factor appearing exactly once between the two numbers, which stops being true once a third number enters the picture.
Up to 10 positive integers, each up to 10³⁰. If the running LCM crosses that ceiling during the calculation, the tool stops and flags that the result is too large to display.
Because adding a number that already divides the running LCM changes nothing: in LCM(6, 10, 15), the pair LCM(6,10) already gives 30, and 15 divides 30 exactly, so the final result stays at 30.
Numbers
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