The HCF and Euclid’s algorithm
The quickest route to the highest common factor is Euclid’s algorithm: divide the larger number by the smaller and repeat with the remainder until the remainder is zero. The last non-zero divisor is the HCF.
HCF and LCM calculators
Highest common factor and lowest common multiple for any list of numbers — with the prime factorisation shown next to the answer.
The LCM via the HCF
The lowest common multiple follows from LCM(a, b) = (a · b) ÷ HCF(a, b). That is why both calculators print the other value beside the answer — each one follows from the other.
Frequently asked questions
Factorise both into primes and multiply the shared factors, or use Euclid’s algorithm. The HCF of 12 and 18 is 6.
Divide the product of the numbers by their HCF. For 12 and 18: (12 · 18) ÷ 6 = 36.
Chiefly for simplifying fractions — dividing the numerator and denominator by the HCF puts the fraction into lowest terms in one step.
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