What is the Least Common Multiple of 78360 and 78375?

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 78360 and 78375 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 78360 and 78375, than apply into the LCM equation.

GCF(78360,78375) = 15
LCM(78360,78375) = ( 78360 × 78375) / 15
LCM(78360,78375) = 6141465000 / 15
LCM(78360,78375) = 409431000

Least Common Multiple (LCM) of 78360 and 78375 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 78360 and 78375. First we will calculate the prime factors of 78360 and 78375.

Prime Factorization of 78360

Prime Factorization of 78375

Now multiplying the highest exponent prime factors to calculate the LCM of 78360 and 78375.

LCM(78360,78375) = 2³ × 3¹ × 5³ × 653¹ × 11¹ × 19¹
LCM(78360,78375) = 409431000