What is the Least Common Multiple of 39504 and 39514?

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 39514 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 39514, than apply into the LCM equation.

GCF(39504,39514) = 2
LCM(39504,39514) = ( 39504 × 39514) / 2
LCM(39504,39514) = 1560961056 / 2
LCM(39504,39514) = 780480528

Least Common Multiple (LCM) of 39504 and 39514 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 39504 and 39514. First we will calculate the prime factors of 39504 and 39514.

Prime Factorization of 39504

Prime Factorization of 39514

Now multiplying the highest exponent prime factors to calculate the LCM of 39504 and 39514.

LCM(39504,39514) = 2⁴ × 3¹ × 823¹ × 23¹ × 859¹
LCM(39504,39514) = 780480528