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What is the Least Common Multiple of 30783 and 30798?

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 30783 and 30798 is 316018278.

LCM(30783,30798) = 316018278

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Least Common Multiple of 30783 and 30798 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30783 and 30798, than apply into the LCM equation.

GCF(30783,30798) = 3
LCM(30783,30798) = ( 30783 × 30798) / 3
LCM(30783,30798) = 948054834 / 3
LCM(30783,30798) = 316018278

Least Common Multiple (LCM) of 30783 and 30798 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30783 and 30798. First we will calculate the prime factors of 30783 and 30798.

Prime Factorization of 30783

Prime factors of 30783 are 3, 31, 331. Prime factorization of 30783 in exponential form is:

30783 = 31 × 311 × 3311

Prime Factorization of 30798

Prime factors of 30798 are 2, 3, 29, 59. Prime factorization of 30798 in exponential form is:

30798 = 21 × 32 × 291 × 591

Now multiplying the highest exponent prime factors to calculate the LCM of 30783 and 30798.

LCM(30783,30798) = 32 × 311 × 3311 × 21 × 291 × 591
LCM(30783,30798) = 316018278