What is the Least Common Multiple of 2034 and 2054?

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 2034 and 2054 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2034 and 2054, than apply into the LCM equation.

GCF(2034,2054) = 2
LCM(2034,2054) = ( 2034 × 2054) / 2
LCM(2034,2054) = 4177836 / 2
LCM(2034,2054) = 2088918

Least Common Multiple (LCM) of 2034 and 2054 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 2034 and 2054. First we will calculate the prime factors of 2034 and 2054.

Prime Factorization of 2034

Prime Factorization of 2054

Now multiplying the highest exponent prime factors to calculate the LCM of 2034 and 2054.

LCM(2034,2054) = 2¹ × 3² × 113¹ × 13¹ × 79¹
LCM(2034,2054) = 2088918