What is the Least Common Multiple of 30504 and 30519?

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 30519 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 30519, than apply into the LCM equation.

GCF(30504,30519) = 3
LCM(30504,30519) = ( 30504 × 30519) / 3
LCM(30504,30519) = 930951576 / 3
LCM(30504,30519) = 310317192

Least Common Multiple (LCM) of 30504 and 30519 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30504 and 30519. First we will calculate the prime factors of 30504 and 30519.

Prime Factorization of 30504

Prime Factorization of 30519

Now multiplying the highest exponent prime factors to calculate the LCM of 30504 and 30519.

LCM(30504,30519) = 2³ × 3² × 31¹ × 41¹ × 3391¹
LCM(30504,30519) = 310317192