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What is the Least Common Multiple of 12004 and 12021?

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 (LCM) of 12004 and 12021 is 144300084.

LCM(12004,12021) = 144300084

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Least Common Multiple of 12004 and 12021 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 12004 and 12021, than apply into the LCM equation.

GCF(12004,12021) = 1
LCM(12004,12021) = ( 12004 × 12021) / 1
LCM(12004,12021) = 144300084 / 1
LCM(12004,12021) = 144300084

Least Common Multiple (LCM) of 12004 and 12021 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 12004 and 12021. First we will calculate the prime factors of 12004 and 12021.

Prime Factorization of 12004

Prime factors of 12004 are 2, 3001. Prime factorization of 12004 in exponential form is:

12004 = 22 × 30011

Prime Factorization of 12021

Prime factors of 12021 are 3, 4007. Prime factorization of 12021 in exponential form is:

12021 = 31 × 40071

Now multiplying the highest exponent prime factors to calculate the LCM of 12004 and 12021.

LCM(12004,12021) = 22 × 30011 × 31 × 40071
LCM(12004,12021) = 144300084