What is the Least Common Multiple of 48075 and 48084?

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 48075 and 48084 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 48075 and 48084, than apply into the LCM equation.

GCF(48075,48084) = 3
LCM(48075,48084) = ( 48075 × 48084) / 3
LCM(48075,48084) = 2311638300 / 3
LCM(48075,48084) = 770546100

Least Common Multiple (LCM) of 48075 and 48084 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 48075 and 48084. First we will calculate the prime factors of 48075 and 48084.

Prime Factorization of 48075

Prime Factorization of 48084

Now multiplying the highest exponent prime factors to calculate the LCM of 48075 and 48084.

LCM(48075,48084) = 3¹ × 5² × 641¹ × 2² × 4007¹
LCM(48075,48084) = 770546100