What is the Least Common Multiple of 48084 and 48100?

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 48084 and 48100 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 48084 and 48100, than apply into the LCM equation.

GCF(48084,48100) = 4
LCM(48084,48100) = ( 48084 × 48100) / 4
LCM(48084,48100) = 2312840400 / 4
LCM(48084,48100) = 578210100

Least Common Multiple (LCM) of 48084 and 48100 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 48084 and 48100. First we will calculate the prime factors of 48084 and 48100.

Prime Factorization of 48084

Prime Factorization of 48100

Now multiplying the highest exponent prime factors to calculate the LCM of 48084 and 48100.

LCM(48084,48100) = 2² × 3¹ × 4007¹ × 5² × 13¹ × 37¹
LCM(48084,48100) = 578210100