What is the Least Common Multiple of 30375 and 30384?

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 30375 and 30384 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30375 and 30384, than apply into the LCM equation.

GCF(30375,30384) = 9
LCM(30375,30384) = ( 30375 × 30384) / 9
LCM(30375,30384) = 922914000 / 9
LCM(30375,30384) = 102546000

Least Common Multiple (LCM) of 30375 and 30384 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30375 and 30384. First we will calculate the prime factors of 30375 and 30384.

Prime Factorization of 30375

Prime Factorization of 30384

Now multiplying the highest exponent prime factors to calculate the LCM of 30375 and 30384.

LCM(30375,30384) = 3⁵ × 5³ × 2⁴ × 211¹
LCM(30375,30384) = 102546000