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What is the Least Common Multiple of 54396 and 54414?

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 54396 and 54414 is 164439108.

LCM(54396,54414) = 164439108

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Least Common Multiple of 54396 and 54414 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 54396 and 54414, than apply into the LCM equation.

GCF(54396,54414) = 18
LCM(54396,54414) = ( 54396 × 54414) / 18
LCM(54396,54414) = 2959903944 / 18
LCM(54396,54414) = 164439108

Least Common Multiple (LCM) of 54396 and 54414 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 54396 and 54414. First we will calculate the prime factors of 54396 and 54414.

Prime Factorization of 54396

Prime factors of 54396 are 2, 3, 1511. Prime factorization of 54396 in exponential form is:

54396 = 22 × 32 × 15111

Prime Factorization of 54414

Prime factors of 54414 are 2, 3, 3023. Prime factorization of 54414 in exponential form is:

54414 = 21 × 32 × 30231

Now multiplying the highest exponent prime factors to calculate the LCM of 54396 and 54414.

LCM(54396,54414) = 22 × 32 × 15111 × 30231
LCM(54396,54414) = 164439108