What is the Least Common Multiple of 30000 and 30015?

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 30000 and 30015 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30000 and 30015, than apply into the LCM equation.

GCF(30000,30015) = 15
LCM(30000,30015) = ( 30000 × 30015) / 15
LCM(30000,30015) = 900450000 / 15
LCM(30000,30015) = 60030000

Least Common Multiple (LCM) of 30000 and 30015 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30000 and 30015. First we will calculate the prime factors of 30000 and 30015.

Prime Factorization of 30000

Prime Factorization of 30015

Now multiplying the highest exponent prime factors to calculate the LCM of 30000 and 30015.

LCM(30000,30015) = 2⁴ × 3² × 5⁴ × 23¹ × 29¹
LCM(30000,30015) = 60030000