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What is the Least Common Multiple of 27078 and 27084?

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 27078 and 27084 is 122230092.

LCM(27078,27084) = 122230092

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Least Common Multiple of 27078 and 27084 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 27078 and 27084, than apply into the LCM equation.

GCF(27078,27084) = 6
LCM(27078,27084) = ( 27078 × 27084) / 6
LCM(27078,27084) = 733380552 / 6
LCM(27078,27084) = 122230092

Least Common Multiple (LCM) of 27078 and 27084 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 27078 and 27084. First we will calculate the prime factors of 27078 and 27084.

Prime Factorization of 27078

Prime factors of 27078 are 2, 3, 4513. Prime factorization of 27078 in exponential form is:

27078 = 21 × 31 × 45131

Prime Factorization of 27084

Prime factors of 27084 are 2, 3, 37, 61. Prime factorization of 27084 in exponential form is:

27084 = 22 × 31 × 371 × 611

Now multiplying the highest exponent prime factors to calculate the LCM of 27078 and 27084.

LCM(27078,27084) = 22 × 31 × 45131 × 371 × 611
LCM(27078,27084) = 122230092