What is the Least Common Multiple of 2019 and 2038?

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 2019 and 2038 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2019 and 2038, than apply into the LCM equation.

GCF(2019,2038) = 1
LCM(2019,2038) = ( 2019 × 2038) / 1
LCM(2019,2038) = 4114722 / 1
LCM(2019,2038) = 4114722

Least Common Multiple (LCM) of 2019 and 2038 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 2019 and 2038. First we will calculate the prime factors of 2019 and 2038.

Prime Factorization of 2019

Prime Factorization of 2038

Now multiplying the highest exponent prime factors to calculate the LCM of 2019 and 2038.

LCM(2019,2038) = 3¹ × 673¹ × 2¹ × 1019¹
LCM(2019,2038) = 4114722