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What is the Least Common Multiple of 30105 and 30111?

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 30105 and 30111 is 302163885.

LCM(30105,30111) = 302163885

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Least Common Multiple of 30105 and 30111 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30105 and 30111, than apply into the LCM equation.

GCF(30105,30111) = 3
LCM(30105,30111) = ( 30105 × 30111) / 3
LCM(30105,30111) = 906491655 / 3
LCM(30105,30111) = 302163885

Least Common Multiple (LCM) of 30105 and 30111 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30105 and 30111. First we will calculate the prime factors of 30105 and 30111.

Prime Factorization of 30105

Prime factors of 30105 are 3, 5, 223. Prime factorization of 30105 in exponential form is:

30105 = 33 × 51 × 2231

Prime Factorization of 30111

Prime factors of 30111 are 3, 10037. Prime factorization of 30111 in exponential form is:

30111 = 31 × 100371

Now multiplying the highest exponent prime factors to calculate the LCM of 30105 and 30111.

LCM(30105,30111) = 33 × 51 × 2231 × 100371
LCM(30105,30111) = 302163885