What is the Least Common Multiple of 57504 and 57519?

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 57504 and 57519 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 57504 and 57519, than apply into the LCM equation.

GCF(57504,57519) = 3
LCM(57504,57519) = ( 57504 × 57519) / 3
LCM(57504,57519) = 3307572576 / 3
LCM(57504,57519) = 1102524192

Least Common Multiple (LCM) of 57504 and 57519 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 57504 and 57519. First we will calculate the prime factors of 57504 and 57519.

Prime Factorization of 57504

Prime Factorization of 57519

Now multiplying the highest exponent prime factors to calculate the LCM of 57504 and 57519.

LCM(57504,57519) = 2⁵ × 3² × 599¹ × 7¹ × 11¹ × 83¹
LCM(57504,57519) = 1102524192