What is the Least Common Multiple of 39504 and 39519?

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 39504 and 39519 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 39504 and 39519, than apply into the LCM equation.

GCF(39504,39519) = 3
LCM(39504,39519) = ( 39504 × 39519) / 3
LCM(39504,39519) = 1561158576 / 3
LCM(39504,39519) = 520386192

Least Common Multiple (LCM) of 39504 and 39519 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 39504 and 39519. First we will calculate the prime factors of 39504 and 39519.

Prime Factorization of 39504

Prime Factorization of 39519

Now multiplying the highest exponent prime factors to calculate the LCM of 39504 and 39519.

LCM(39504,39519) = 2⁴ × 3² × 823¹ × 4391¹
LCM(39504,39519) = 520386192