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What is the Least Common Multiple of 12138 and 12144?

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 12138 and 12144 is 24567312.

LCM(12138,12144) = 24567312

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Least Common Multiple of 12138 and 12144 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 12138 and 12144, than apply into the LCM equation.

GCF(12138,12144) = 6
LCM(12138,12144) = ( 12138 × 12144) / 6
LCM(12138,12144) = 147403872 / 6
LCM(12138,12144) = 24567312

Least Common Multiple (LCM) of 12138 and 12144 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 12138 and 12144. First we will calculate the prime factors of 12138 and 12144.

Prime Factorization of 12138

Prime factors of 12138 are 2, 3, 7, 17. Prime factorization of 12138 in exponential form is:

12138 = 21 × 31 × 71 × 172

Prime Factorization of 12144

Prime factors of 12144 are 2, 3, 11, 23. Prime factorization of 12144 in exponential form is:

12144 = 24 × 31 × 111 × 231

Now multiplying the highest exponent prime factors to calculate the LCM of 12138 and 12144.

LCM(12138,12144) = 24 × 31 × 71 × 172 × 111 × 231
LCM(12138,12144) = 24567312