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What is the Least Common Multiple of 5805 and 5820?

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 5805 and 5820 is 2252340.

LCM(5805,5820) = 2252340

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Least Common Multiple of 5805 and 5820 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 5805 and 5820, than apply into the LCM equation.

GCF(5805,5820) = 15
LCM(5805,5820) = ( 5805 × 5820) / 15
LCM(5805,5820) = 33785100 / 15
LCM(5805,5820) = 2252340

Least Common Multiple (LCM) of 5805 and 5820 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 5805 and 5820. First we will calculate the prime factors of 5805 and 5820.

Prime Factorization of 5805

Prime factors of 5805 are 3, 5, 43. Prime factorization of 5805 in exponential form is:

5805 = 33 × 51 × 431

Prime Factorization of 5820

Prime factors of 5820 are 2, 3, 5, 97. Prime factorization of 5820 in exponential form is:

5820 = 22 × 31 × 51 × 971

Now multiplying the highest exponent prime factors to calculate the LCM of 5805 and 5820.

LCM(5805,5820) = 33 × 51 × 431 × 22 × 971
LCM(5805,5820) = 2252340