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What is the Least Common Multiple of 30115 and 30135?

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 30115 and 30135 is 181503105.

LCM(30115,30135) = 181503105

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Least Common Multiple of 30115 and 30135 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30115 and 30135, than apply into the LCM equation.

GCF(30115,30135) = 5
LCM(30115,30135) = ( 30115 × 30135) / 5
LCM(30115,30135) = 907515525 / 5
LCM(30115,30135) = 181503105

Least Common Multiple (LCM) of 30115 and 30135 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30115 and 30135. First we will calculate the prime factors of 30115 and 30135.

Prime Factorization of 30115

Prime factors of 30115 are 5, 19, 317. Prime factorization of 30115 in exponential form is:

30115 = 51 × 191 × 3171

Prime Factorization of 30135

Prime factors of 30135 are 3, 5, 7, 41. Prime factorization of 30135 in exponential form is:

30135 = 31 × 51 × 72 × 411

Now multiplying the highest exponent prime factors to calculate the LCM of 30115 and 30135.

LCM(30115,30135) = 51 × 191 × 3171 × 31 × 72 × 411
LCM(30115,30135) = 181503105