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What is the Least Common Multiple of 54175 and 54180?

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 54175 and 54180 is 587040300.

LCM(54175,54180) = 587040300

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Least Common Multiple of 54175 and 54180 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 54175 and 54180, than apply into the LCM equation.

GCF(54175,54180) = 5
LCM(54175,54180) = ( 54175 × 54180) / 5
LCM(54175,54180) = 2935201500 / 5
LCM(54175,54180) = 587040300

Least Common Multiple (LCM) of 54175 and 54180 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 54175 and 54180. First we will calculate the prime factors of 54175 and 54180.

Prime Factorization of 54175

Prime factors of 54175 are 5, 11, 197. Prime factorization of 54175 in exponential form is:

54175 = 52 × 111 × 1971

Prime Factorization of 54180

Prime factors of 54180 are 2, 3, 5, 7, 43. Prime factorization of 54180 in exponential form is:

54180 = 22 × 32 × 51 × 71 × 431

Now multiplying the highest exponent prime factors to calculate the LCM of 54175 and 54180.

LCM(54175,54180) = 52 × 111 × 1971 × 22 × 32 × 71 × 431
LCM(54175,54180) = 587040300