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What is the Least Common Multiple of 30585 and 30596?

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 30585 and 30596 is 935778660.

LCM(30585,30596) = 935778660

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Least Common Multiple of 30585 and 30596 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30585 and 30596, than apply into the LCM equation.

GCF(30585,30596) = 1
LCM(30585,30596) = ( 30585 × 30596) / 1
LCM(30585,30596) = 935778660 / 1
LCM(30585,30596) = 935778660

Least Common Multiple (LCM) of 30585 and 30596 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30585 and 30596. First we will calculate the prime factors of 30585 and 30596.

Prime Factorization of 30585

Prime factors of 30585 are 3, 5, 2039. Prime factorization of 30585 in exponential form is:

30585 = 31 × 51 × 20391

Prime Factorization of 30596

Prime factors of 30596 are 2, 7649. Prime factorization of 30596 in exponential form is:

30596 = 22 × 76491

Now multiplying the highest exponent prime factors to calculate the LCM of 30585 and 30596.

LCM(30585,30596) = 31 × 51 × 20391 × 22 × 76491
LCM(30585,30596) = 935778660