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What is the Least Common Multiple of 12048 and 12057?

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 12048 and 12057 is 48420912.

LCM(12048,12057) = 48420912

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Least Common Multiple of 12048 and 12057 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 12048 and 12057, than apply into the LCM equation.

GCF(12048,12057) = 3
LCM(12048,12057) = ( 12048 × 12057) / 3
LCM(12048,12057) = 145262736 / 3
LCM(12048,12057) = 48420912

Least Common Multiple (LCM) of 12048 and 12057 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 12048 and 12057. First we will calculate the prime factors of 12048 and 12057.

Prime Factorization of 12048

Prime factors of 12048 are 2, 3, 251. Prime factorization of 12048 in exponential form is:

12048 = 24 × 31 × 2511

Prime Factorization of 12057

Prime factors of 12057 are 3, 4019. Prime factorization of 12057 in exponential form is:

12057 = 31 × 40191

Now multiplying the highest exponent prime factors to calculate the LCM of 12048 and 12057.

LCM(12048,12057) = 24 × 31 × 2511 × 40191
LCM(12048,12057) = 48420912