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What is the Least Common Multiple of 30400 and 30404?

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 30400 and 30404 is 231070400.

LCM(30400,30404) = 231070400

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Least Common Multiple of 30400 and 30404 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30400 and 30404, than apply into the LCM equation.

GCF(30400,30404) = 4
LCM(30400,30404) = ( 30400 × 30404) / 4
LCM(30400,30404) = 924281600 / 4
LCM(30400,30404) = 231070400

Least Common Multiple (LCM) of 30400 and 30404 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30400 and 30404. First we will calculate the prime factors of 30400 and 30404.

Prime Factorization of 30400

Prime factors of 30400 are 2, 5, 19. Prime factorization of 30400 in exponential form is:

30400 = 26 × 52 × 191

Prime Factorization of 30404

Prime factors of 30404 are 2, 11, 691. Prime factorization of 30404 in exponential form is:

30404 = 22 × 111 × 6911

Now multiplying the highest exponent prime factors to calculate the LCM of 30400 and 30404.

LCM(30400,30404) = 26 × 52 × 191 × 111 × 6911
LCM(30400,30404) = 231070400