What is the Least Common Multiple of 54384 and 54390?

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 54384 and 54390 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 54384 and 54390, than apply into the LCM equation.

GCF(54384,54390) = 6
LCM(54384,54390) = ( 54384 × 54390) / 6
LCM(54384,54390) = 2957945760 / 6
LCM(54384,54390) = 492990960

Least Common Multiple (LCM) of 54384 and 54390 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 54384 and 54390. First we will calculate the prime factors of 54384 and 54390.

Prime Factorization of 54384

Prime Factorization of 54390

Now multiplying the highest exponent prime factors to calculate the LCM of 54384 and 54390.

LCM(54384,54390) = 2⁴ × 3¹ × 11¹ × 103¹ × 5¹ × 7² × 37¹
LCM(54384,54390) = 492990960