What is the Least Common Multiple of 2054 and 2072?

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 2054 and 2072 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2054 and 2072, than apply into the LCM equation.

GCF(2054,2072) = 2
LCM(2054,2072) = ( 2054 × 2072) / 2
LCM(2054,2072) = 4255888 / 2
LCM(2054,2072) = 2127944

Least Common Multiple (LCM) of 2054 and 2072 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 2054 and 2072. First we will calculate the prime factors of 2054 and 2072.

Prime Factorization of 2054

Prime Factorization of 2072

Now multiplying the highest exponent prime factors to calculate the LCM of 2054 and 2072.

LCM(2054,2072) = 2³ × 13¹ × 79¹ × 7¹ × 37¹
LCM(2054,2072) = 2127944