What is the Least Common Multiple of 19008 and 19023?

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 19008 and 19023 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 19008 and 19023, than apply into the LCM equation.

GCF(19008,19023) = 3
LCM(19008,19023) = ( 19008 × 19023) / 3
LCM(19008,19023) = 361589184 / 3
LCM(19008,19023) = 120529728

Least Common Multiple (LCM) of 19008 and 19023 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 19008 and 19023. First we will calculate the prime factors of 19008 and 19023.

Prime Factorization of 19008

Prime Factorization of 19023

Now multiplying the highest exponent prime factors to calculate the LCM of 19008 and 19023.

LCM(19008,19023) = 2⁶ × 3³ × 11¹ × 17¹ × 373¹
LCM(19008,19023) = 120529728