What is the Least Common Multiple of 30375 and 30380?

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 30375 and 30380 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30375 and 30380, than apply into the LCM equation.

GCF(30375,30380) = 5
LCM(30375,30380) = ( 30375 × 30380) / 5
LCM(30375,30380) = 922792500 / 5
LCM(30375,30380) = 184558500

Least Common Multiple (LCM) of 30375 and 30380 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30375 and 30380. First we will calculate the prime factors of 30375 and 30380.

Prime Factorization of 30375

Prime Factorization of 30380

Now multiplying the highest exponent prime factors to calculate the LCM of 30375 and 30380.

LCM(30375,30380) = 3⁵ × 5³ × 2² × 7² × 31¹
LCM(30375,30380) = 184558500