What is the Least Common Multiple of 30744 and 30750?

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 30744 and 30750 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30744 and 30750, than apply into the LCM equation.

GCF(30744,30750) = 6
LCM(30744,30750) = ( 30744 × 30750) / 6
LCM(30744,30750) = 945378000 / 6
LCM(30744,30750) = 157563000

Least Common Multiple (LCM) of 30744 and 30750 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30744 and 30750. First we will calculate the prime factors of 30744 and 30750.

Prime Factorization of 30744

Prime Factorization of 30750

Now multiplying the highest exponent prime factors to calculate the LCM of 30744 and 30750.

LCM(30744,30750) = 2³ × 3² × 7¹ × 61¹ × 5³ × 41¹
LCM(30744,30750) = 157563000