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What is the Least Common Multiple of 30891 and 30900?

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 30891 and 30900 is 318177300.

LCM(30891,30900) = 318177300

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Least Common Multiple of 30891 and 30900 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30891 and 30900, than apply into the LCM equation.

GCF(30891,30900) = 3
LCM(30891,30900) = ( 30891 × 30900) / 3
LCM(30891,30900) = 954531900 / 3
LCM(30891,30900) = 318177300

Least Common Multiple (LCM) of 30891 and 30900 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30891 and 30900. First we will calculate the prime factors of 30891 and 30900.

Prime Factorization of 30891

Prime factors of 30891 are 3, 7, 1471. Prime factorization of 30891 in exponential form is:

30891 = 31 × 71 × 14711

Prime Factorization of 30900

Prime factors of 30900 are 2, 3, 5, 103. Prime factorization of 30900 in exponential form is:

30900 = 22 × 31 × 52 × 1031

Now multiplying the highest exponent prime factors to calculate the LCM of 30891 and 30900.

LCM(30891,30900) = 31 × 71 × 14711 × 22 × 52 × 1031
LCM(30891,30900) = 318177300