What is the Least Common Multiple of 39360 and 39375?

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 39360 and 39375 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 39360 and 39375, than apply into the LCM equation.

GCF(39360,39375) = 15
LCM(39360,39375) = ( 39360 × 39375) / 15
LCM(39360,39375) = 1549800000 / 15
LCM(39360,39375) = 103320000

Least Common Multiple (LCM) of 39360 and 39375 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 39360 and 39375. First we will calculate the prime factors of 39360 and 39375.

Prime Factorization of 39360

Prime Factorization of 39375

Now multiplying the highest exponent prime factors to calculate the LCM of 39360 and 39375.

LCM(39360,39375) = 2⁶ × 3² × 5⁴ × 41¹ × 7¹
LCM(39360,39375) = 103320000