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What is the Least Common Multiple of 29584 and 29600?

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 29584 and 29600 is 54730400.

LCM(29584,29600) = 54730400

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Least Common Multiple of 29584 and 29600 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 29584 and 29600, than apply into the LCM equation.

GCF(29584,29600) = 16
LCM(29584,29600) = ( 29584 × 29600) / 16
LCM(29584,29600) = 875686400 / 16
LCM(29584,29600) = 54730400

Least Common Multiple (LCM) of 29584 and 29600 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 29584 and 29600. First we will calculate the prime factors of 29584 and 29600.

Prime Factorization of 29584

Prime factors of 29584 are 2, 43. Prime factorization of 29584 in exponential form is:

29584 = 24 × 432

Prime Factorization of 29600

Prime factors of 29600 are 2, 5, 37. Prime factorization of 29600 in exponential form is:

29600 = 25 × 52 × 371

Now multiplying the highest exponent prime factors to calculate the LCM of 29584 and 29600.

LCM(29584,29600) = 25 × 432 × 52 × 371
LCM(29584,29600) = 54730400