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What is the Least Common Multiple of 13110 and 13128?

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 13110 and 13128 is 28684680.

LCM(13110,13128) = 28684680

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Least Common Multiple of 13110 and 13128 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13110 and 13128, than apply into the LCM equation.

GCF(13110,13128) = 6
LCM(13110,13128) = ( 13110 × 13128) / 6
LCM(13110,13128) = 172108080 / 6
LCM(13110,13128) = 28684680

Least Common Multiple (LCM) of 13110 and 13128 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13110 and 13128. First we will calculate the prime factors of 13110 and 13128.

Prime Factorization of 13110

Prime factors of 13110 are 2, 3, 5, 19, 23. Prime factorization of 13110 in exponential form is:

13110 = 21 × 31 × 51 × 191 × 231

Prime Factorization of 13128

Prime factors of 13128 are 2, 3, 547. Prime factorization of 13128 in exponential form is:

13128 = 23 × 31 × 5471

Now multiplying the highest exponent prime factors to calculate the LCM of 13110 and 13128.

LCM(13110,13128) = 23 × 31 × 51 × 191 × 231 × 5471
LCM(13110,13128) = 28684680