What is the Least Common Multiple of 2004 and 2022?

Least common multiple or lowest common denominator (lcd) can be calculated in two way; with the LCM formula calculation of greatest common factor (GCF), or multiplying the prime factors with the highest exponent factor.

Least Common Multiple of 2004 and 2022 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2004 and 2022, than apply into the LCM equation.

GCF(2004,2022) = 6
LCM(2004,2022) = ( 2004 × 2022) / 6
LCM(2004,2022) = 4052088 / 6
LCM(2004,2022) = 675348

Least Common Multiple (LCM) of 2004 and 2022 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 2004 and 2022. First we will calculate the prime factors of 2004 and 2022.

Prime Factorization of 2004

Prime Factorization of 2022

Now multiplying the highest exponent prime factors to calculate the LCM of 2004 and 2022.

LCM(2004,2022) = 2² × 3¹ × 167¹ × 337¹
LCM(2004,2022) = 675348