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What is the Least Common Multiple of 54315 and 54324?

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 54315 and 54324 is 327845340.

LCM(54315,54324) = 327845340

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Least Common Multiple of 54315 and 54324 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 54315 and 54324, than apply into the LCM equation.

GCF(54315,54324) = 9
LCM(54315,54324) = ( 54315 × 54324) / 9
LCM(54315,54324) = 2950608060 / 9
LCM(54315,54324) = 327845340

Least Common Multiple (LCM) of 54315 and 54324 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 54315 and 54324. First we will calculate the prime factors of 54315 and 54324.

Prime Factorization of 54315

Prime factors of 54315 are 3, 5, 17, 71. Prime factorization of 54315 in exponential form is:

54315 = 32 × 51 × 171 × 711

Prime Factorization of 54324

Prime factors of 54324 are 2, 3, 503. Prime factorization of 54324 in exponential form is:

54324 = 22 × 33 × 5031

Now multiplying the highest exponent prime factors to calculate the LCM of 54315 and 54324.

LCM(54315,54324) = 33 × 51 × 171 × 711 × 22 × 5031
LCM(54315,54324) = 327845340