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What is the Least Common Multiple of 30578 and 30584?

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 30578 and 30584 is 467598776.

LCM(30578,30584) = 467598776

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Least Common Multiple of 30578 and 30584 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30578 and 30584, than apply into the LCM equation.

GCF(30578,30584) = 2
LCM(30578,30584) = ( 30578 × 30584) / 2
LCM(30578,30584) = 935197552 / 2
LCM(30578,30584) = 467598776

Least Common Multiple (LCM) of 30578 and 30584 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30578 and 30584. First we will calculate the prime factors of 30578 and 30584.

Prime Factorization of 30578

Prime factors of 30578 are 2, 15289. Prime factorization of 30578 in exponential form is:

30578 = 21 × 152891

Prime Factorization of 30584

Prime factors of 30584 are 2, 3823. Prime factorization of 30584 in exponential form is:

30584 = 23 × 38231

Now multiplying the highest exponent prime factors to calculate the LCM of 30578 and 30584.

LCM(30578,30584) = 23 × 152891 × 38231
LCM(30578,30584) = 467598776