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What is the Least Common Multiple of 30597 and 30609?

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 30597 and 30609 is 312181191.

LCM(30597,30609) = 312181191

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Least Common Multiple of 30597 and 30609 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30597 and 30609, than apply into the LCM equation.

GCF(30597,30609) = 3
LCM(30597,30609) = ( 30597 × 30609) / 3
LCM(30597,30609) = 936543573 / 3
LCM(30597,30609) = 312181191

Least Common Multiple (LCM) of 30597 and 30609 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30597 and 30609. First we will calculate the prime factors of 30597 and 30609.

Prime Factorization of 30597

Prime factors of 30597 are 3, 7, 31, 47. Prime factorization of 30597 in exponential form is:

30597 = 31 × 71 × 311 × 471

Prime Factorization of 30609

Prime factors of 30609 are 3, 19, 179. Prime factorization of 30609 in exponential form is:

30609 = 32 × 191 × 1791

Now multiplying the highest exponent prime factors to calculate the LCM of 30597 and 30609.

LCM(30597,30609) = 32 × 71 × 311 × 471 × 191 × 1791
LCM(30597,30609) = 312181191