What is the Least Common Multiple of 54375 and 54384?

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 54375 and 54384 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 54375 and 54384, than apply into the LCM equation.

GCF(54375,54384) = 3
LCM(54375,54384) = ( 54375 × 54384) / 3
LCM(54375,54384) = 2957130000 / 3
LCM(54375,54384) = 985710000

Least Common Multiple (LCM) of 54375 and 54384 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 54375 and 54384. First we will calculate the prime factors of 54375 and 54384.

Prime Factorization of 54375

Prime Factorization of 54384

Now multiplying the highest exponent prime factors to calculate the LCM of 54375 and 54384.

LCM(54375,54384) = 3¹ × 5⁴ × 29¹ × 2⁴ × 11¹ × 103¹
LCM(54375,54384) = 985710000