What is the Least Common Multiple of 12003 and 12012?

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 12003 and 12012 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 12003 and 12012, than apply into the LCM equation.

GCF(12003,12012) = 3
LCM(12003,12012) = ( 12003 × 12012) / 3
LCM(12003,12012) = 144180036 / 3
LCM(12003,12012) = 48060012

Least Common Multiple (LCM) of 12003 and 12012 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 12003 and 12012. First we will calculate the prime factors of 12003 and 12012.

Prime Factorization of 12003

Prime Factorization of 12012

Now multiplying the highest exponent prime factors to calculate the LCM of 12003 and 12012.

LCM(12003,12012) = 3¹ × 4001¹ × 2² × 7¹ × 11¹ × 13¹
LCM(12003,12012) = 48060012