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What is the Least Common Multiple of 30895 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 30895 and 30900 is 190931100.

LCM(30895,30900) = 190931100

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Least Common Multiple of 30895 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 30895 and 30900, than apply into the LCM equation.

GCF(30895,30900) = 5
LCM(30895,30900) = ( 30895 × 30900) / 5
LCM(30895,30900) = 954655500 / 5
LCM(30895,30900) = 190931100

Least Common Multiple (LCM) of 30895 and 30900 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30895 and 30900. First we will calculate the prime factors of 30895 and 30900.

Prime Factorization of 30895

Prime factors of 30895 are 5, 37, 167. Prime factorization of 30895 in exponential form is:

30895 = 51 × 371 × 1671

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 30895 and 30900.

LCM(30895,30900) = 52 × 371 × 1671 × 22 × 31 × 1031
LCM(30895,30900) = 190931100