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What is the Least Common Multiple of 12126 and 12135?

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 12126 and 12135 is 49049670.

LCM(12126,12135) = 49049670

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Least Common Multiple of 12126 and 12135 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 12126 and 12135, than apply into the LCM equation.

GCF(12126,12135) = 3
LCM(12126,12135) = ( 12126 × 12135) / 3
LCM(12126,12135) = 147149010 / 3
LCM(12126,12135) = 49049670

Least Common Multiple (LCM) of 12126 and 12135 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 12126 and 12135. First we will calculate the prime factors of 12126 and 12135.

Prime Factorization of 12126

Prime factors of 12126 are 2, 3, 43, 47. Prime factorization of 12126 in exponential form is:

12126 = 21 × 31 × 431 × 471

Prime Factorization of 12135

Prime factors of 12135 are 3, 5, 809. Prime factorization of 12135 in exponential form is:

12135 = 31 × 51 × 8091

Now multiplying the highest exponent prime factors to calculate the LCM of 12126 and 12135.

LCM(12126,12135) = 21 × 31 × 431 × 471 × 51 × 8091
LCM(12126,12135) = 49049670