LCM and HCF Explained (with Simple Examples)

LCM and HCF are two of the most useful ideas in arithmetic, and they come up everywhere from fractions to scheduling.

HCF (Highest Common Factor)

The largest number that divides all your numbers exactly. For 12 and 18, the HCF is 6. It's used to simplify fractions.

LCM (Lowest Common Multiple)

The smallest number that all your numbers divide into. For 12 and 18, the LCM is 36. It's used to add fractions with different denominators, and to solve "when do two events line up?" problems.

A quick method

Break each number into prime factors. The HCF multiplies the common factors; the LCM multiplies the highest power of every factor that appears.

Calculate instantly

Use our LCM & HCF Calculator for any set of numbers. Working with fractions? Try the Fraction Calculator, and check divisibility with the Prime Number Checker.