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What is the Least Common Multiple of 54309 and 54314?

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 54309 and 54314 is 2949739026.

LCM(54309,54314) = 2949739026

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Least Common Multiple of 54309 and 54314 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 54309 and 54314, than apply into the LCM equation.

GCF(54309,54314) = 1
LCM(54309,54314) = ( 54309 × 54314) / 1
LCM(54309,54314) = 2949739026 / 1
LCM(54309,54314) = 2949739026

Least Common Multiple (LCM) of 54309 and 54314 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 54309 and 54314. First we will calculate the prime factors of 54309 and 54314.

Prime Factorization of 54309

Prime factors of 54309 are 3, 43, 421. Prime factorization of 54309 in exponential form is:

54309 = 31 × 431 × 4211

Prime Factorization of 54314

Prime factors of 54314 are 2, 13, 2089. Prime factorization of 54314 in exponential form is:

54314 = 21 × 131 × 20891

Now multiplying the highest exponent prime factors to calculate the LCM of 54309 and 54314.

LCM(54309,54314) = 31 × 431 × 4211 × 21 × 131 × 20891
LCM(54309,54314) = 2949739026