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What is the Least Common Multiple of 54078 and 54090?

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 54078 and 54090 is 487513170.

LCM(54078,54090) = 487513170

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Least Common Multiple of 54078 and 54090 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 54078 and 54090, than apply into the LCM equation.

GCF(54078,54090) = 6
LCM(54078,54090) = ( 54078 × 54090) / 6
LCM(54078,54090) = 2925079020 / 6
LCM(54078,54090) = 487513170

Least Common Multiple (LCM) of 54078 and 54090 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 54078 and 54090. First we will calculate the prime factors of 54078 and 54090.

Prime Factorization of 54078

Prime factors of 54078 are 2, 3, 9013. Prime factorization of 54078 in exponential form is:

54078 = 21 × 31 × 90131

Prime Factorization of 54090

Prime factors of 54090 are 2, 3, 5, 601. Prime factorization of 54090 in exponential form is:

54090 = 21 × 32 × 51 × 6011

Now multiplying the highest exponent prime factors to calculate the LCM of 54078 and 54090.

LCM(54078,54090) = 21 × 32 × 90131 × 51 × 6011
LCM(54078,54090) = 487513170