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What is the Least Common Multiple of 27192 and 27210?

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 27192 and 27210 is 123315720.

LCM(27192,27210) = 123315720

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Least Common Multiple of 27192 and 27210 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 27192 and 27210, than apply into the LCM equation.

GCF(27192,27210) = 6
LCM(27192,27210) = ( 27192 × 27210) / 6
LCM(27192,27210) = 739894320 / 6
LCM(27192,27210) = 123315720

Least Common Multiple (LCM) of 27192 and 27210 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 27192 and 27210. First we will calculate the prime factors of 27192 and 27210.

Prime Factorization of 27192

Prime factors of 27192 are 2, 3, 11, 103. Prime factorization of 27192 in exponential form is:

27192 = 23 × 31 × 111 × 1031

Prime Factorization of 27210

Prime factors of 27210 are 2, 3, 5, 907. Prime factorization of 27210 in exponential form is:

27210 = 21 × 31 × 51 × 9071

Now multiplying the highest exponent prime factors to calculate the LCM of 27192 and 27210.

LCM(27192,27210) = 23 × 31 × 111 × 1031 × 51 × 9071
LCM(27192,27210) = 123315720