Calculate the Least Common Multiple (LCM) and Greatest Common Factor (GCF/GCD) for up to 6 numbers. Shows prime factorisation and step-by-step working.
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At least A and B are required. C through F are optional.
LCM is the smallest number divisible by all inputs. GCF is the largest factor shared by all inputs.
See how each number breaks into prime factors — useful for understanding the result.
The Euclidean algorithm finds GCF efficiently: repeatedly replace the larger number with the remainder when divided by the smaller. When remainder is 0, the last non-zero value is the GCF.
Adding fractions with different denominators (find LCM of denominators). Scheduling problems (when will two events coincide again). Gear ratios, music rhythm calculations.
Simplifying fractions (divide by GCF of numerator and denominator). Splitting things into equal groups. Finding the largest tile size that fits a floor without cutting.
They are the same thing. GCF = Greatest Common Factor. GCD = Greatest Common Divisor. Different textbooks use different terms for identical concepts.
GCF(12,18) = 6. LCM = 12×18÷6 = 36. Verify: 36÷12=3 (whole), 36÷18=2 (whole). 36 is the smallest number divisible by both 12 and 18.
GCF of 12 and 18: factors of 12 are 1,2,3,4,6,12 and factors of 18 are 1,2,3,6,9,18. The largest common factor is 6.