☰ Contents1.2 · The Fundamental Theorem of Arithmetic28/101

The HCF / LCM machine

Enter any numbers and watch the HCF and LCM fall straight out of the primes — common primes at the smallest power, all primes at the greatest.

HCF / LCM machine · read it off the primes

6=2 × 3
20=22 × 5
HCF = 2 = 2common primes · smallest power
LCM = 22 × 3 × 5 = 60all primes · greatest power
Shortcut holds: HCF × LCM = 2 × 60 = 120 = 6 × 20. For two numbers, HCF × LCM always equals their product.