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What is the Least Common Multiple of 30378 and 30382?

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 30378 and 30382 is 461472198.

LCM(30378,30382) = 461472198

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Least Common Multiple of 30378 and 30382 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30378 and 30382, than apply into the LCM equation.

GCF(30378,30382) = 2
LCM(30378,30382) = ( 30378 × 30382) / 2
LCM(30378,30382) = 922944396 / 2
LCM(30378,30382) = 461472198

Least Common Multiple (LCM) of 30378 and 30382 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30378 and 30382. First we will calculate the prime factors of 30378 and 30382.

Prime Factorization of 30378

Prime factors of 30378 are 2, 3, 61, 83. Prime factorization of 30378 in exponential form is:

30378 = 21 × 31 × 611 × 831

Prime Factorization of 30382

Prime factors of 30382 are 2, 11, 1381. Prime factorization of 30382 in exponential form is:

30382 = 21 × 111 × 13811

Now multiplying the highest exponent prime factors to calculate the LCM of 30378 and 30382.

LCM(30378,30382) = 21 × 31 × 611 × 831 × 111 × 13811
LCM(30378,30382) = 461472198