What is the Least Common Multiple of 54000 and 54014?

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 54014 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 54014, than apply into the LCM equation.

GCF(54000,54014) = 2
LCM(54000,54014) = ( 54000 × 54014) / 2
LCM(54000,54014) = 2916756000 / 2
LCM(54000,54014) = 1458378000

Least Common Multiple (LCM) of 54000 and 54014 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 54000 and 54014. First we will calculate the prime factors of 54000 and 54014.

Prime Factorization of 54000

Prime Factorization of 54014

Now multiplying the highest exponent prime factors to calculate the LCM of 54000 and 54014.

LCM(54000,54014) = 2⁴ × 3³ × 5³ × 113¹ × 239¹
LCM(54000,54014) = 1458378000