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What is the Least Common Multiple of 18392 and 18400?

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 18392 and 18400 is 42301600.

LCM(18392,18400) = 42301600

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Least Common Multiple of 18392 and 18400 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 18392 and 18400, than apply into the LCM equation.

GCF(18392,18400) = 8
LCM(18392,18400) = ( 18392 × 18400) / 8
LCM(18392,18400) = 338412800 / 8
LCM(18392,18400) = 42301600

Least Common Multiple (LCM) of 18392 and 18400 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 18392 and 18400. First we will calculate the prime factors of 18392 and 18400.

Prime Factorization of 18392

Prime factors of 18392 are 2, 11, 19. Prime factorization of 18392 in exponential form is:

18392 = 23 × 112 × 191

Prime Factorization of 18400

Prime factors of 18400 are 2, 5, 23. Prime factorization of 18400 in exponential form is:

18400 = 25 × 52 × 231

Now multiplying the highest exponent prime factors to calculate the LCM of 18392 and 18400.

LCM(18392,18400) = 25 × 112 × 191 × 52 × 231
LCM(18392,18400) = 42301600