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What is the Least Common Multiple of 54012 and 54030?

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 54012 and 54030 is 486378060.

LCM(54012,54030) = 486378060

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Least Common Multiple of 54012 and 54030 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 54012 and 54030, than apply into the LCM equation.

GCF(54012,54030) = 6
LCM(54012,54030) = ( 54012 × 54030) / 6
LCM(54012,54030) = 2918268360 / 6
LCM(54012,54030) = 486378060

Least Common Multiple (LCM) of 54012 and 54030 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 54012 and 54030. First we will calculate the prime factors of 54012 and 54030.

Prime Factorization of 54012

Prime factors of 54012 are 2, 3, 7, 643. Prime factorization of 54012 in exponential form is:

54012 = 22 × 31 × 71 × 6431

Prime Factorization of 54030

Prime factors of 54030 are 2, 3, 5, 1801. Prime factorization of 54030 in exponential form is:

54030 = 21 × 31 × 51 × 18011

Now multiplying the highest exponent prime factors to calculate the LCM of 54012 and 54030.

LCM(54012,54030) = 22 × 31 × 71 × 6431 × 51 × 18011
LCM(54012,54030) = 486378060