Maths Help UK

Lowest common multiple and highest common factor

LCM = smallest number both divide into. HCF = largest number that divides both.

Enter values above to calculate.

Two ways to find LCM/HCF. Listing: write multiples (for LCM) or factors (for HCF) until you find the smallest common one. Prime factors: take the lower (HCF) or higher (LCM) power of each prime.

Worked examples
HCF(12, 18) = 6. 12 = 2²×3, 18 = 2×3². HCF takes lower powers: 2×3=6.
LCM(12, 18) = 36. Higher powers: 2²×3²=36.
HCF(a, b) × LCM(a, b) = a × b. Useful sanity check.
Related: Prime factor decomposition Squares and cubes Indices (introduction) Standard form

Frequently asked questions

When do I use LCM vs HCF?
LCM: scheduling problems (when do two events recur together). HCF: simplifying fractions or grouping quantities into largest equal lots.
Three numbers?
Same prime-factor method — take the lowest (HCF) or highest (LCM) power across all three.