What is the Least Common Multiple of 30504 and 30514?

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 30504 and 30514 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30504 and 30514, than apply into the LCM equation.

GCF(30504,30514) = 2
LCM(30504,30514) = ( 30504 × 30514) / 2
LCM(30504,30514) = 930799056 / 2
LCM(30504,30514) = 465399528

Least Common Multiple (LCM) of 30504 and 30514 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30504 and 30514. First we will calculate the prime factors of 30504 and 30514.

Prime Factorization of 30504

Prime Factorization of 30514

Now multiplying the highest exponent prime factors to calculate the LCM of 30504 and 30514.

LCM(30504,30514) = 2³ × 3¹ × 31¹ × 41¹ × 11¹ × 19¹ × 73¹
LCM(30504,30514) = 465399528