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What is the Least Common Multiple of 30270 and 30286?

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 30270 and 30286 is 458378610.

LCM(30270,30286) = 458378610

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Least Common Multiple of 30270 and 30286 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30270 and 30286, than apply into the LCM equation.

GCF(30270,30286) = 2
LCM(30270,30286) = ( 30270 × 30286) / 2
LCM(30270,30286) = 916757220 / 2
LCM(30270,30286) = 458378610

Least Common Multiple (LCM) of 30270 and 30286 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30270 and 30286. First we will calculate the prime factors of 30270 and 30286.

Prime Factorization of 30270

Prime factors of 30270 are 2, 3, 5, 1009. Prime factorization of 30270 in exponential form is:

30270 = 21 × 31 × 51 × 10091

Prime Factorization of 30286

Prime factors of 30286 are 2, 19, 797. Prime factorization of 30286 in exponential form is:

30286 = 21 × 191 × 7971

Now multiplying the highest exponent prime factors to calculate the LCM of 30270 and 30286.

LCM(30270,30286) = 21 × 31 × 51 × 10091 × 191 × 7971
LCM(30270,30286) = 458378610