Prime factors do the work
Write each number as a product of primes. HCF takes the lowest power of each common prime; LCM takes the highest power of every prime that appears.
Worked example
For 36 and 48: 36 = 2² × 3² and 48 = 2⁴ × 3. HCF = 2² × 3 = 12. LCM = 2⁴ × 3² = 144. Check: HCF × LCM = 12 × 144 = 1,728, which equals 36 × 48.
Typical word problems
Bells ringing together again, or tiles of the largest equal size, are LCM and HCF problems respectively. Decide which by asking whether you are looking for the first meeting time (LCM) or the largest equal division (HCF).
Where else it helps
This topic strengthens ratio problems and appears in railway mathematics.
