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What is the Least Common Multiple of 30591 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 30591 and 30609 is 104039991.

LCM(30591,30609) = 104039991

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Least Common Multiple of 30591 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 30591 and 30609, than apply into the LCM equation.

GCF(30591,30609) = 9
LCM(30591,30609) = ( 30591 × 30609) / 9
LCM(30591,30609) = 936359919 / 9
LCM(30591,30609) = 104039991

Least Common Multiple (LCM) of 30591 and 30609 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30591 and 30609. First we will calculate the prime factors of 30591 and 30609.

Prime Factorization of 30591

Prime factors of 30591 are 3, 11, 103. Prime factorization of 30591 in exponential form is:

30591 = 33 × 111 × 1031

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 30591 and 30609.

LCM(30591,30609) = 33 × 111 × 1031 × 191 × 1791
LCM(30591,30609) = 104039991