What is the Least Common Multiple of 54000 and 54012?

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 54000 and 54012 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 54000 and 54012, than apply into the LCM equation.

GCF(54000,54012) = 12
LCM(54000,54012) = ( 54000 × 54012) / 12
LCM(54000,54012) = 2916648000 / 12
LCM(54000,54012) = 243054000

Least Common Multiple (LCM) of 54000 and 54012 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 54000 and 54012. First we will calculate the prime factors of 54000 and 54012.

Prime Factorization of 54000

Prime Factorization of 54012

Now multiplying the highest exponent prime factors to calculate the LCM of 54000 and 54012.

LCM(54000,54012) = 2⁴ × 3³ × 5³ × 7¹ × 643¹
LCM(54000,54012) = 243054000