What is the Least Common Multiple of 30750 and 30768?

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 30750 and 30768 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30750 and 30768, than apply into the LCM equation.

GCF(30750,30768) = 6
LCM(30750,30768) = ( 30750 × 30768) / 6
LCM(30750,30768) = 946116000 / 6
LCM(30750,30768) = 157686000

Least Common Multiple (LCM) of 30750 and 30768 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30750 and 30768. First we will calculate the prime factors of 30750 and 30768.

Prime Factorization of 30750

Prime Factorization of 30768

Now multiplying the highest exponent prime factors to calculate the LCM of 30750 and 30768.

LCM(30750,30768) = 2⁴ × 3¹ × 5³ × 41¹ × 641¹
LCM(30750,30768) = 157686000