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What is the Least Common Multiple of 30051 and 30065?

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 30051 and 30065 is 129069045.

LCM(30051,30065) = 129069045

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Least Common Multiple of 30051 and 30065 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30051 and 30065, than apply into the LCM equation.

GCF(30051,30065) = 7
LCM(30051,30065) = ( 30051 × 30065) / 7
LCM(30051,30065) = 903483315 / 7
LCM(30051,30065) = 129069045

Least Common Multiple (LCM) of 30051 and 30065 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30051 and 30065. First we will calculate the prime factors of 30051 and 30065.

Prime Factorization of 30051

Prime factors of 30051 are 3, 7, 53. Prime factorization of 30051 in exponential form is:

30051 = 34 × 71 × 531

Prime Factorization of 30065

Prime factors of 30065 are 5, 7, 859. Prime factorization of 30065 in exponential form is:

30065 = 51 × 71 × 8591

Now multiplying the highest exponent prime factors to calculate the LCM of 30051 and 30065.

LCM(30051,30065) = 34 × 71 × 531 × 51 × 8591
LCM(30051,30065) = 129069045