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What is the Least Common Multiple of 30205 and 30225?

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 30205 and 30225 is 182589225.

LCM(30205,30225) = 182589225

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Least Common Multiple of 30205 and 30225 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30205 and 30225, than apply into the LCM equation.

GCF(30205,30225) = 5
LCM(30205,30225) = ( 30205 × 30225) / 5
LCM(30205,30225) = 912946125 / 5
LCM(30205,30225) = 182589225

Least Common Multiple (LCM) of 30205 and 30225 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30205 and 30225. First we will calculate the prime factors of 30205 and 30225.

Prime Factorization of 30205

Prime factors of 30205 are 5, 7, 863. Prime factorization of 30205 in exponential form is:

30205 = 51 × 71 × 8631

Prime Factorization of 30225

Prime factors of 30225 are 3, 5, 13, 31. Prime factorization of 30225 in exponential form is:

30225 = 31 × 52 × 131 × 311

Now multiplying the highest exponent prime factors to calculate the LCM of 30205 and 30225.

LCM(30205,30225) = 52 × 71 × 8631 × 31 × 131 × 311
LCM(30205,30225) = 182589225