GCD and LCM

Once two numbers have been factorised into primes, the greatest common divisor and the least common multiple can be read off directly from the factorisations.

Property — GCD and LCM

Given $a,b\in\mathbb{N}$, factorised into primes:

• GCD$(a,b)$: product of the common factors with the smaller exponent.
• LCM$(a,b)$: product of all the factors with the larger exponent.

The GCD takes only what the two numbers have in common, “rounding down”; the LCM takes everything, “rounding up”.

Links

Topics: Numbers and operations
Concepts: Prime factorisation · Greatest common divisor (GCD) · Least common multiple (LCM)
Skills: Factorise