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What is the Least Common Multiple of 54036 and 54054?

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 54036 and 54054 is 162270108.

LCM(54036,54054) = 162270108

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Least Common Multiple of 54036 and 54054 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 54036 and 54054, than apply into the LCM equation.

GCF(54036,54054) = 18
LCM(54036,54054) = ( 54036 × 54054) / 18
LCM(54036,54054) = 2920861944 / 18
LCM(54036,54054) = 162270108

Least Common Multiple (LCM) of 54036 and 54054 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 54036 and 54054. First we will calculate the prime factors of 54036 and 54054.

Prime Factorization of 54036

Prime factors of 54036 are 2, 3, 19, 79. Prime factorization of 54036 in exponential form is:

54036 = 22 × 32 × 191 × 791

Prime Factorization of 54054

Prime factors of 54054 are 2, 3, 7, 11, 13. Prime factorization of 54054 in exponential form is:

54054 = 21 × 33 × 71 × 111 × 131

Now multiplying the highest exponent prime factors to calculate the LCM of 54036 and 54054.

LCM(54036,54054) = 22 × 33 × 191 × 791 × 71 × 111 × 131
LCM(54036,54054) = 162270108