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What is the Least Common Multiple of 12132 and 12150?

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 12132 and 12150 is 8189100.

LCM(12132,12150) = 8189100

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Least Common Multiple of 12132 and 12150 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 12132 and 12150, than apply into the LCM equation.

GCF(12132,12150) = 18
LCM(12132,12150) = ( 12132 × 12150) / 18
LCM(12132,12150) = 147403800 / 18
LCM(12132,12150) = 8189100

Least Common Multiple (LCM) of 12132 and 12150 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 12132 and 12150. First we will calculate the prime factors of 12132 and 12150.

Prime Factorization of 12132

Prime factors of 12132 are 2, 3, 337. Prime factorization of 12132 in exponential form is:

12132 = 22 × 32 × 3371

Prime Factorization of 12150

Prime factors of 12150 are 2, 3, 5. Prime factorization of 12150 in exponential form is:

12150 = 21 × 35 × 52

Now multiplying the highest exponent prime factors to calculate the LCM of 12132 and 12150.

LCM(12132,12150) = 22 × 35 × 3371 × 52
LCM(12132,12150) = 8189100