What is the Least Common Multiple of 30078 and 30084?

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 30078 and 30084 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30078 and 30084, than apply into the LCM equation.

GCF(30078,30084) = 6
LCM(30078,30084) = ( 30078 × 30084) / 6
LCM(30078,30084) = 904866552 / 6
LCM(30078,30084) = 150811092

Least Common Multiple (LCM) of 30078 and 30084 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30078 and 30084. First we will calculate the prime factors of 30078 and 30084.

Prime Factorization of 30078

Prime Factorization of 30084

Now multiplying the highest exponent prime factors to calculate the LCM of 30078 and 30084.

LCM(30078,30084) = 2² × 3³ × 557¹ × 23¹ × 109¹
LCM(30078,30084) = 150811092