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What is the Least Common Multiple of 30900 and 30904?

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 30900 and 30904 is 238733400.

LCM(30900,30904) = 238733400

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Least Common Multiple of 30900 and 30904 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30900 and 30904, than apply into the LCM equation.

GCF(30900,30904) = 4
LCM(30900,30904) = ( 30900 × 30904) / 4
LCM(30900,30904) = 954933600 / 4
LCM(30900,30904) = 238733400

Least Common Multiple (LCM) of 30900 and 30904 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30900 and 30904. First we will calculate the prime factors of 30900 and 30904.

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

Prime Factorization of 30904

Prime factors of 30904 are 2, 3863. Prime factorization of 30904 in exponential form is:

30904 = 23 × 38631

Now multiplying the highest exponent prime factors to calculate the LCM of 30900 and 30904.

LCM(30900,30904) = 23 × 31 × 52 × 1031 × 38631
LCM(30900,30904) = 238733400