What is the Least Common Multiple of 39504 and 39516?

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 39516 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 39516, than apply into the LCM equation.

GCF(39504,39516) = 12
LCM(39504,39516) = ( 39504 × 39516) / 12
LCM(39504,39516) = 1561040064 / 12
LCM(39504,39516) = 130086672

Least Common Multiple (LCM) of 39504 and 39516 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 39504 and 39516. First we will calculate the prime factors of 39504 and 39516.

Prime Factorization of 39504

Prime Factorization of 39516

Now multiplying the highest exponent prime factors to calculate the LCM of 39504 and 39516.

LCM(39504,39516) = 2⁴ × 3¹ × 823¹ × 37¹ × 89¹
LCM(39504,39516) = 130086672