What is the Least Common Multiple of 30003 and 30012?

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 30003 and 30012 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30003 and 30012, than apply into the LCM equation.

GCF(30003,30012) = 3
LCM(30003,30012) = ( 30003 × 30012) / 3
LCM(30003,30012) = 900450036 / 3
LCM(30003,30012) = 300150012

Least Common Multiple (LCM) of 30003 and 30012 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30003 and 30012. First we will calculate the prime factors of 30003 and 30012.

Prime Factorization of 30003

Prime Factorization of 30012

Now multiplying the highest exponent prime factors to calculate the LCM of 30003 and 30012.

LCM(30003,30012) = 3¹ × 73¹ × 137¹ × 2² × 41¹ × 61¹
LCM(30003,30012) = 300150012