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What is the Least Common Multiple of 54300 and 54312?

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 54300 and 54312 is 245761800.

LCM(54300,54312) = 245761800

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Least Common Multiple of 54300 and 54312 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 54300 and 54312, than apply into the LCM equation.

GCF(54300,54312) = 12
LCM(54300,54312) = ( 54300 × 54312) / 12
LCM(54300,54312) = 2949141600 / 12
LCM(54300,54312) = 245761800

Least Common Multiple (LCM) of 54300 and 54312 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 54300 and 54312. First we will calculate the prime factors of 54300 and 54312.

Prime Factorization of 54300

Prime factors of 54300 are 2, 3, 5, 181. Prime factorization of 54300 in exponential form is:

54300 = 22 × 31 × 52 × 1811

Prime Factorization of 54312

Prime factors of 54312 are 2, 3, 31, 73. Prime factorization of 54312 in exponential form is:

54312 = 23 × 31 × 311 × 731

Now multiplying the highest exponent prime factors to calculate the LCM of 54300 and 54312.

LCM(54300,54312) = 23 × 31 × 52 × 1811 × 311 × 731
LCM(54300,54312) = 245761800