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What is the Least Common Multiple of 12039 and 12054?

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 12039 and 12054 is 48372702.

LCM(12039,12054) = 48372702

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Least Common Multiple of 12039 and 12054 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 12039 and 12054, than apply into the LCM equation.

GCF(12039,12054) = 3
LCM(12039,12054) = ( 12039 × 12054) / 3
LCM(12039,12054) = 145118106 / 3
LCM(12039,12054) = 48372702

Least Common Multiple (LCM) of 12039 and 12054 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 12039 and 12054. First we will calculate the prime factors of 12039 and 12054.

Prime Factorization of 12039

Prime factors of 12039 are 3, 4013. Prime factorization of 12039 in exponential form is:

12039 = 31 × 40131

Prime Factorization of 12054

Prime factors of 12054 are 2, 3, 7, 41. Prime factorization of 12054 in exponential form is:

12054 = 21 × 31 × 72 × 411

Now multiplying the highest exponent prime factors to calculate the LCM of 12039 and 12054.

LCM(12039,12054) = 31 × 40131 × 21 × 72 × 411
LCM(12039,12054) = 48372702